%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO303^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:08:52 PM UTC 2025 % Result : Theorem 3.80s 3.98s % Output : Proof 3.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO303^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n021.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 12:59:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.80/3.98 SZS status Theorem for theBenchmark.p % 3.80/3.98 SZS output start Proof for theBenchmark.p % 3.80/3.98 Clause #0 (by assumption #[]): Eq % 3.80/3.98 (Not % 3.80/3.98 ((∀ (P : Iota → Prop), Or (Not (P c0)) (∀ (Xx : Iota), P Xx)) → Or (Not (And (cS c0) (cT c0))) (And (cT a) (cS b)))) % 3.80/3.98 True % 3.80/3.98 Clause #1 (by clausification #[0]): Eq ((∀ (P : Iota → Prop), Or (Not (P c0)) (∀ (Xx : Iota), P Xx)) → Or (Not (And (cS c0) (cT c0))) (And (cT a) (cS b))) % 3.80/3.98 False % 3.80/3.98 Clause #2 (by clausification #[1]): Eq (∀ (P : Iota → Prop), Or (Not (P c0)) (∀ (Xx : Iota), P Xx)) True % 3.80/3.98 Clause #3 (by clausification #[1]): Eq (Or (Not (And (cS c0) (cT c0))) (And (cT a) (cS b))) False % 3.80/3.98 Clause #4 (by clausification #[2]): ∀ (a : Iota → Prop), Eq (Or (Not (a c0)) (∀ (Xx : Iota), a Xx)) True % 3.80/3.98 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop), Or (Eq (Not (a c0)) True) (Eq (∀ (Xx : Iota), a Xx) True) % 3.80/3.98 Clause #6 (by clausification #[5]): ∀ (a : Iota → Prop), Or (Eq (∀ (Xx : Iota), a Xx) True) (Eq (a c0) False) % 3.80/3.98 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a c0) False) (Eq (a a_1) True) % 3.80/3.98 Clause #13 (by fluidLoobHoist #[7]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a a_1) True) (Or (Eq True False) (Eq (a c0) False)) % 3.80/3.98 Clause #16 (by clausification #[13]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a a_1) True) (Eq (a c0) False) % 3.80/3.98 Clause #22 (by clausification #[3]): Eq (And (cT a) (cS b)) False % 3.80/3.98 Clause #23 (by clausification #[3]): Eq (Not (And (cS c0) (cT c0))) False % 3.80/3.98 Clause #24 (by clausification #[22]): Or (Eq (cT a) False) (Eq (cS b) False) % 3.80/3.98 Clause #30 (by clausification #[23]): Eq (And (cS c0) (cT c0)) True % 3.80/3.98 Clause #31 (by clausification #[30]): Eq (cT c0) True % 3.80/3.98 Clause #32 (by clausification #[30]): Eq (cS c0) True % 3.80/3.98 Clause #35 (by fluidSup #[31, 16]): ∀ (a : Iota), Or (Eq ((fun x => cT x) a) True) (Eq ((fun _ => _) True) False) % 3.80/3.98 Clause #42 (by fluidSup #[32, 7]): ∀ (a : Iota), Or (Eq ((fun _ => _) True) False) (Eq ((fun x => cS x) a) True) % 3.80/3.98 Clause #47 (by betaEtaReduce #[42]): ∀ (a : Iota), Or (Eq True False) (Eq (cS a) True) % 3.80/3.98 Clause #48 (by clausification #[47]): ∀ (a : Iota), Eq (cS a) True % 3.80/3.98 Clause #49 (by backward demodulation #[48, 24]): Or (Eq (cT a) False) (Eq True False) % 3.80/3.98 Clause #54 (by clausification #[49]): Eq (cT a) False % 3.80/3.98 Clause #76 (by betaEtaReduce #[35]): ∀ (a : Iota), Or (Eq (cT a) True) (Eq True False) % 3.80/3.98 Clause #77 (by clausification #[76]): ∀ (a : Iota), Eq (cT a) True % 3.80/3.98 Clause #78 (by superposition #[77, 54]): Eq True False % 3.80/3.98 Clause #85 (by clausification #[78]): False % 3.80/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------