%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU541^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:01:52 PM UTC 2025 % Result : Theorem 3.82s 3.98s % Output : Proof 3.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU541^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.14 % Command : duper %s % 0.13/0.35 % Computer : n031.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 : Fri Oct 3 06:26:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.82/3.98 SZS status Theorem for theBenchmark.p % 3.82/3.98 SZS output start Proof for theBenchmark.p % 3.82/3.98 Clause #0 (by assumption #[]): Eq (Eq prop2setI (∀ (Xphi : Prop), Xphi → in emptyset (prop2set Xphi))) True % 3.82/3.98 Clause #1 (by assumption #[]): Eq (Eq set2prop fun A => in emptyset A) True % 3.82/3.98 Clause #2 (by assumption #[]): Eq (Not (prop2setI → ∀ (Xphi : Prop), Xphi → set2prop (prop2set Xphi))) True % 3.82/3.98 Clause #3 (by clausification #[2]): Eq (prop2setI → ∀ (Xphi : Prop), Xphi → set2prop (prop2set Xphi)) False % 3.82/3.98 Clause #4 (by clausification #[3]): Eq prop2setI True % 3.82/3.98 Clause #5 (by clausification #[3]): Eq (∀ (Xphi : Prop), Xphi → set2prop (prop2set Xphi)) False % 3.82/3.98 Clause #6 (by clausification #[5]): ∀ (a : Prop), Eq (Not (skS.0 0 a → set2prop (prop2set (skS.0 0 a)))) True % 3.82/3.98 Clause #7 (by clausification #[6]): ∀ (a : Prop), Eq (skS.0 0 a → set2prop (prop2set (skS.0 0 a))) False % 3.82/3.98 Clause #8 (by clausification #[7]): ∀ (a : Prop), Eq (skS.0 0 a) True % 3.82/3.98 Clause #9 (by clausification #[7]): ∀ (a : Prop), Eq (set2prop (prop2set (skS.0 0 a))) False % 3.82/3.98 Clause #11 (by identity boolHoist #[8]): ∀ (a : Prop), Or (Eq (skS.0 0 False) True) (Eq a True) % 3.82/3.98 Clause #14 (by equality factoring #[11]): Or (Ne True True) (Eq (skS.0 0 False) True) % 3.82/3.98 Clause #16 (by clausification #[0]): Eq prop2setI (∀ (Xphi : Prop), Xphi → in emptyset (prop2set Xphi)) % 3.82/3.98 Clause #17 (by bool simp #[16]): Eq prop2setI (And (True → in emptyset (prop2set True)) (False → in emptyset (prop2set False))) % 3.82/3.98 Clause #18 (by bool simp #[17]): Eq prop2setI (And (True → in emptyset (prop2set True)) True) % 3.82/3.98 Clause #19 (by bool simp #[18]): Eq prop2setI (True → in emptyset (prop2set True)) % 3.82/3.98 Clause #20 (by bool simp #[19]): Eq prop2setI (in emptyset (prop2set True)) % 3.82/3.98 Clause #21 (by forward demodulation #[20, 4]): Eq True (in emptyset (prop2set True)) % 3.82/3.98 Clause #25 (by clausification #[14]): Or (Eq (skS.0 0 False) True) (Or (Eq True False) (Eq True False)) % 3.82/3.98 Clause #27 (by clausification #[25]): Or (Eq (skS.0 0 False) True) (Eq True False) % 3.82/3.98 Clause #28 (by clausification #[27]): Eq (skS.0 0 False) True % 3.82/3.98 Clause #29 (by identity loobHoist #[9]): ∀ (a : Prop), Or (Eq (set2prop (prop2set True)) False) (Eq (skS.0 0 a) False) % 3.82/3.98 Clause #32 (by identity boolHoist #[29]): ∀ (a : Prop), Or (Eq (set2prop (prop2set True)) False) (Or (Eq (skS.0 0 False) False) (Eq a True)) % 3.82/3.98 Clause #33 (by betaEtaReduce #[1]): Eq (Eq set2prop (in emptyset)) True % 3.82/3.98 Clause #34 (by clausification #[33]): Eq set2prop (in emptyset) % 3.82/3.98 Clause #35 (by argument congruence #[34]): ∀ (a : Iota), Eq (set2prop a) (in emptyset a) % 3.82/3.98 Clause #40 (by superposition #[35, 21]): Eq True (set2prop (prop2set True)) % 3.82/3.98 Clause #51 (by forward demodulation #[32, 40]): ∀ (a : Prop), Or (Eq True False) (Or (Eq (skS.0 0 False) False) (Eq a True)) % 3.82/3.98 Clause #52 (by clausification #[51]): ∀ (a : Prop), Or (Eq (skS.0 0 False) False) (Eq a True) % 3.82/3.98 Clause #53 (by superposition #[52, 28]): ∀ (a : Prop), Or (Eq a True) (Eq False True) % 3.82/3.98 Clause #54 (by clausification #[53]): ∀ (a : Prop), Eq a True % 3.82/3.98 Clause #57 (by falseElim #[54]): False % 3.82/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------