TSTP Solution File: SEU769^2 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU769^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 16:43:48 EDT 2023
% Result : Theorem 8.19s 8.38s
% Output : Proof 8.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU769^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n028.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 16:53:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 8.19/8.38 SZS status Theorem for theBenchmark.p
% 8.19/8.38 SZS output start Proof for theBenchmark.p
% 8.19/8.38 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx))
% 8.19/8.38 True
% 8.19/8.38 Clause #3 (by assumption #[]): Eq (Eq breln1Set fun A => dsetconstr (powerset (cartprod A A)) fun R => breln1 A R) True
% 8.19/8.38 Clause #4 (by assumption #[]): Eq (Not (dsetconstrER → ∀ (A R : Iota), in R (breln1Set A) → breln1 A R)) True
% 8.19/8.38 Clause #5 (by clausification #[4]): Eq (dsetconstrER → ∀ (A R : Iota), in R (breln1Set A) → breln1 A R) False
% 8.19/8.38 Clause #6 (by clausification #[5]): Eq dsetconstrER True
% 8.19/8.38 Clause #7 (by clausification #[5]): Eq (∀ (A R : Iota), in R (breln1Set A) → breln1 A R) False
% 8.19/8.38 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (R : Iota), in R (breln1Set (skS.0 0 a)) → breln1 (skS.0 0 a) R)) True
% 8.19/8.38 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (R : Iota), in R (breln1Set (skS.0 0 a)) → breln1 (skS.0 0 a) R) False
% 8.19/8.38 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 1 a a_1) (breln1Set (skS.0 0 a)) → breln1 (skS.0 0 a) (skS.0 1 a a_1))) True
% 8.19/8.38 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (breln1Set (skS.0 0 a)) → breln1 (skS.0 0 a) (skS.0 1 a a_1)) False
% 8.19/8.38 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (breln1Set (skS.0 0 a))) True
% 8.19/8.38 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) False
% 8.19/8.38 Clause #14 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True
% 8.19/8.38 Clause #15 (by clausification #[14]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)
% 8.19/8.38 Clause #16 (by forward demodulation #[15, 6]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)
% 8.19/8.38 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True
% 8.19/8.38 Clause #18 (by clausification #[17]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True
% 8.19/8.38 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True
% 8.19/8.38 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True)
% 8.19/8.38 Clause #58 (by betaEtaReduce #[3]): Eq (Eq breln1Set fun A => dsetconstr (powerset (cartprod A A)) (breln1 A)) True
% 8.19/8.38 Clause #59 (by clausification #[58]): Eq breln1Set fun A => dsetconstr (powerset (cartprod A A)) (breln1 A)
% 8.19/8.38 Clause #60 (by argument congruence #[59]): ∀ (a : Iota), Eq (breln1Set a) ((fun A => dsetconstr (powerset (cartprod A A)) (breln1 A)) a)
% 8.19/8.38 Clause #65 (by betaEtaReduce #[60]): ∀ (a : Iota), Eq (breln1Set a) (dsetconstr (powerset (cartprod a a)) (breln1 a))
% 8.19/8.38 Clause #66 (by superposition #[65, 20]): ∀ (a a_1 : Iota), Or (Eq (in a (breln1Set a_1)) False) (Eq (breln1 a_1 a) True)
% 8.19/8.38 Clause #74 (by superposition #[66, 12]): ∀ (a a_1 : Iota), Or (Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)
% 8.19/8.38 Clause #1136 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) True
% 8.19/8.38 Clause #1137 (by superposition #[1136, 13]): Eq True False
% 8.19/8.38 Clause #1155 (by clausification #[1137]): False
% 8.19/8.38 SZS output end Proof for theBenchmark.p
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