%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PUZ129+2 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 07:58:23 PM UTC 2025 % Result : Theorem 4.26s 4.44s % Output : Proof 4.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : PUZ129+2 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.15 % Command : duper %s % 0.14/0.36 % Computer : n019.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 20:43:38 EDT 2025 % 0.14/0.37 % CPUTime : % 4.26/4.44 SZS status Theorem for theBenchmark.p % 4.26/4.44 SZS output start Proof for theBenchmark.p % 4.26/4.44 Clause #0 (by assumption #[]): Eq % 4.26/4.44 (Not % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (∀ (A : Iota), % 4.26/4.44 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.26/4.44 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.26/4.44 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.26/4.44 (∀ (E : Iota), % 4.26/4.44 And (grocer E) (property1 E industrious pos) → % 4.26/4.44 Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.26/4.44 (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H))) % 4.26/4.44 (∀ (I : Iota), % 4.26/4.44 And (cyclist I) (property1 I unhealthy pos) → % 4.26/4.44 Exists fun J => And (property1 J dishonest pos) (Eq I J))) % 4.26/4.44 (∀ (K : Iota), % 4.26/4.44 And (person K) (property1 K healthy pos) → % 4.26/4.44 Not (Exists fun L => And (property1 L unhealthy pos) (Eq K L)))) % 4.26/4.44 (∀ (M : Iota), % 4.26/4.44 And (person M) (property1 M honest pos) → Not (Exists fun N => And (property1 N dishonest pos) (Eq M N)))) % 4.26/4.44 (∀ (O : Iota), grocer O → Exists fun P => And (person P) (Eq O P))) % 4.26/4.44 (∀ (Q : Iota), cyclist Q → Exists fun R => And (person R) (Eq Q R)) → % 4.26/4.44 ∀ (S : Iota), grocer S → Not (Exists fun T => And (cyclist T) (Eq S T)))) % 4.26/4.44 True % 4.26/4.44 Clause #1 (by clausification #[0]): Eq % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (∀ (A : Iota), % 4.26/4.44 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.26/4.44 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.26/4.44 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.26/4.44 (∀ (E : Iota), % 4.26/4.44 And (grocer E) (property1 E industrious pos) → % 4.26/4.44 Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.26/4.44 (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H))) % 4.26/4.44 (∀ (I : Iota), % 4.26/4.44 And (cyclist I) (property1 I unhealthy pos) → Exists fun J => And (property1 J dishonest pos) (Eq I J))) % 4.26/4.44 (∀ (K : Iota), % 4.26/4.44 And (person K) (property1 K healthy pos) → % 4.26/4.44 Not (Exists fun L => And (property1 L unhealthy pos) (Eq K L)))) % 4.26/4.44 (∀ (M : Iota), % 4.26/4.44 And (person M) (property1 M honest pos) → Not (Exists fun N => And (property1 N dishonest pos) (Eq M N)))) % 4.26/4.44 (∀ (O : Iota), grocer O → Exists fun P => And (person P) (Eq O P))) % 4.26/4.44 (∀ (Q : Iota), cyclist Q → Exists fun R => And (person R) (Eq Q R)) → % 4.26/4.44 ∀ (S : Iota), grocer S → Not (Exists fun T => And (cyclist T) (Eq S T))) % 4.26/4.44 False % 4.26/4.44 Clause #2 (by clausification #[1]): Eq % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (And % 4.26/4.44 (∀ (A : Iota), % 4.26/4.44 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.26/4.44 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.26/4.44 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.26/4.44 (∀ (E : Iota), % 4.26/4.44 And (grocer E) (property1 E industrious pos) → Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.26/4.44 (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H))) % 4.26/4.44 (∀ (I : Iota), % 4.26/4.44 And (cyclist I) (property1 I unhealthy pos) → Exists fun J => And (property1 J dishonest pos) (Eq I J))) % 4.26/4.44 (∀ (K : Iota), % 4.26/4.44 And (person K) (property1 K healthy pos) → Not (Exists fun L => And (property1 L unhealthy pos) (Eq K L)))) % 4.30/4.46 (∀ (M : Iota), % 4.30/4.46 And (person M) (property1 M honest pos) → Not (Exists fun N => And (property1 N dishonest pos) (Eq M N)))) % 4.30/4.46 (∀ (O : Iota), grocer O → Exists fun P => And (person P) (Eq O P))) % 4.30/4.46 (∀ (Q : Iota), cyclist Q → Exists fun R => And (person R) (Eq Q R))) % 4.30/4.46 True % 4.30/4.46 Clause #3 (by clausification #[1]): Eq (∀ (S : Iota), grocer S → Not (Exists fun T => And (cyclist T) (Eq S T))) False % 4.30/4.46 Clause #5 (by clausification #[2]): Eq % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (∀ (A : Iota), % 4.30/4.46 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.30/4.46 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.30/4.46 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.30/4.46 (∀ (E : Iota), % 4.30/4.46 And (grocer E) (property1 E industrious pos) → Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.30/4.46 (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H))) % 4.30/4.46 (∀ (I : Iota), % 4.30/4.46 And (cyclist I) (property1 I unhealthy pos) → Exists fun J => And (property1 J dishonest pos) (Eq I J))) % 4.30/4.46 (∀ (K : Iota), % 4.30/4.46 And (person K) (property1 K healthy pos) → Not (Exists fun L => And (property1 L unhealthy pos) (Eq K L)))) % 4.30/4.46 (∀ (M : Iota), % 4.30/4.46 And (person M) (property1 M honest pos) → Not (Exists fun N => And (property1 N dishonest pos) (Eq M N)))) % 4.30/4.46 (∀ (O : Iota), grocer O → Exists fun P => And (person P) (Eq O P))) % 4.30/4.46 True % 4.30/4.46 Clause #12 (by clausification #[3]): ∀ (a : Iota), Eq (Not (grocer (skS.0 1 a) → Not (Exists fun T => And (cyclist T) (Eq (skS.0 1 a) T)))) True % 4.30/4.46 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (grocer (skS.0 1 a) → Not (Exists fun T => And (cyclist T) (Eq (skS.0 1 a) T))) False % 4.30/4.46 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (grocer (skS.0 1 a)) True % 4.30/4.46 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (Not (Exists fun T => And (cyclist T) (Eq (skS.0 1 a) T))) False % 4.30/4.46 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (Exists fun T => And (cyclist T) (Eq (skS.0 1 a) T)) True % 4.30/4.46 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (And (cyclist (skS.0 2 a a_1)) (Eq (skS.0 1 a) (skS.0 2 a a_1))) True % 4.30/4.46 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 1 a) (skS.0 2 a a_1)) True % 4.30/4.46 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (cyclist (skS.0 2 a a_1)) True % 4.30/4.46 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (skS.0 1 a) (skS.0 2 a a_1) % 4.30/4.46 Clause #21 (by forward demodulation #[19, 20]): ∀ (a : Iota), Eq (cyclist (skS.0 1 a)) True % 4.30/4.46 Clause #24 (by clausification #[5]): Eq (∀ (O : Iota), grocer O → Exists fun P => And (person P) (Eq O P)) True % 4.30/4.46 Clause #25 (by clausification #[5]): Eq % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (And % 4.30/4.46 (∀ (A : Iota), % 4.30/4.46 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.30/4.46 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.30/4.46 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.30/4.46 (∀ (E : Iota), % 4.30/4.46 And (grocer E) (property1 E industrious pos) → Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.30/4.46 (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H))) % 4.30/4.46 (∀ (I : Iota), % 4.30/4.46 And (cyclist I) (property1 I unhealthy pos) → Exists fun J => And (property1 J dishonest pos) (Eq I J))) % 4.30/4.46 (∀ (K : Iota), % 4.30/4.46 And (person K) (property1 K healthy pos) → Not (Exists fun L => And (property1 L unhealthy pos) (Eq K L)))) % 4.30/4.46 (∀ (M : Iota), % 4.30/4.46 And (person M) (property1 M honest pos) → Not (Exists fun N => And (property1 N dishonest pos) (Eq M N)))) % 4.30/4.46 True % 4.30/4.46 Clause #26 (by clausification #[24]): ∀ (a : Iota), Eq (grocer a → Exists fun P => And (person P) (Eq a P)) True % 4.30/4.49 Clause #27 (by clausification #[26]): ∀ (a : Iota), Or (Eq (grocer a) False) (Eq (Exists fun P => And (person P) (Eq a P)) True) % 4.30/4.49 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (grocer a) False) (Eq (And (person (skS.0 3 a a_1)) (Eq a (skS.0 3 a a_1))) True) % 4.30/4.49 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (grocer a) False) (Eq (Eq a (skS.0 3 a a_1)) True) % 4.30/4.49 Clause #30 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (grocer a) False) (Eq (person (skS.0 3 a a_1)) True) % 4.30/4.49 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (grocer a) False) (Eq a (skS.0 3 a a_1)) % 4.30/4.49 Clause #32 (by superposition #[31, 14]): ∀ (a a_1 : Iota), Or (Eq (skS.0 1 a) (skS.0 3 (skS.0 1 a) a_1)) (Eq False True) % 4.30/4.49 Clause #33 (by superposition #[30, 14]): ∀ (a a_1 : Iota), Or (Eq (person (skS.0 3 (skS.0 1 a) a_1)) True) (Eq False True) % 4.30/4.49 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (person (skS.0 3 (skS.0 1 a) a_1)) True % 4.30/4.49 Clause #36 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (skS.0 1 a) (skS.0 3 (skS.0 1 a) a_1) % 4.30/4.49 Clause #37 (by backward demodulation #[36, 35]): ∀ (a : Iota), Eq (person (skS.0 1 a)) True % 4.30/4.49 Clause #40 (by clausification #[25]): Eq % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (∀ (A : Iota), % 4.30/4.49 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.30/4.49 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.30/4.49 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.30/4.49 (∀ (E : Iota), % 4.30/4.49 And (grocer E) (property1 E industrious pos) → Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.30/4.49 (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H))) % 4.30/4.49 (∀ (I : Iota), % 4.30/4.49 And (cyclist I) (property1 I unhealthy pos) → Exists fun J => And (property1 J dishonest pos) (Eq I J))) % 4.30/4.49 (∀ (K : Iota), % 4.30/4.49 And (person K) (property1 K healthy pos) → Not (Exists fun L => And (property1 L unhealthy pos) (Eq K L)))) % 4.30/4.49 True % 4.30/4.49 Clause #52 (by clausification #[40]): Eq % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (∀ (A : Iota), % 4.30/4.49 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.30/4.49 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.30/4.49 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.30/4.49 (∀ (E : Iota), % 4.30/4.49 And (grocer E) (property1 E industrious pos) → Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.30/4.49 (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H))) % 4.30/4.49 (∀ (I : Iota), % 4.30/4.49 And (cyclist I) (property1 I unhealthy pos) → Exists fun J => And (property1 J dishonest pos) (Eq I J))) % 4.30/4.49 True % 4.30/4.49 Clause #64 (by clausification #[52]): Eq % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (∀ (A : Iota), % 4.30/4.49 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.30/4.49 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.30/4.49 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.30/4.49 (∀ (E : Iota), % 4.30/4.49 And (grocer E) (property1 E industrious pos) → Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.30/4.49 (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H))) % 4.30/4.49 True % 4.30/4.49 Clause #73 (by clausification #[64]): Eq (∀ (G : Iota), cyclist G → Exists fun H => And (property1 H industrious pos) (Eq G H)) True % 4.30/4.49 Clause #74 (by clausification #[64]): Eq % 4.30/4.49 (And % 4.30/4.49 (And % 4.30/4.49 (∀ (A : Iota), % 4.30/4.49 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.30/4.49 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.30/4.49 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.30/4.49 (∀ (E : Iota), % 4.30/4.49 And (grocer E) (property1 E industrious pos) → Exists fun F => And (property1 F honest pos) (Eq E F))) % 4.30/4.51 True % 4.30/4.51 Clause #75 (by clausification #[73]): ∀ (a : Iota), Eq (cyclist a → Exists fun H => And (property1 H industrious pos) (Eq a H)) True % 4.30/4.51 Clause #76 (by clausification #[75]): ∀ (a : Iota), Or (Eq (cyclist a) False) (Eq (Exists fun H => And (property1 H industrious pos) (Eq a H)) True) % 4.30/4.51 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), % 4.30/4.51 Or (Eq (cyclist a) False) (Eq (And (property1 (skS.0 5 a a_1) industrious pos) (Eq a (skS.0 5 a a_1))) True) % 4.30/4.51 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (cyclist a) False) (Eq (Eq a (skS.0 5 a a_1)) True) % 4.30/4.51 Clause #79 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (cyclist a) False) (Eq (property1 (skS.0 5 a a_1) industrious pos) True) % 4.30/4.51 Clause #80 (by clausification #[78]): ∀ (a a_1 : Iota), Or (Eq (cyclist a) False) (Eq a (skS.0 5 a a_1)) % 4.30/4.51 Clause #81 (by superposition #[80, 21]): ∀ (a a_1 : Iota), Or (Eq (skS.0 1 a) (skS.0 5 (skS.0 1 a) a_1)) (Eq False True) % 4.30/4.51 Clause #82 (by superposition #[79, 21]): ∀ (a a_1 : Iota), Or (Eq (property1 (skS.0 5 (skS.0 1 a) a_1) industrious pos) True) (Eq False True) % 4.30/4.51 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Eq (property1 (skS.0 5 (skS.0 1 a) a_1) industrious pos) True % 4.30/4.51 Clause #85 (by clausification #[81]): ∀ (a a_1 : Iota), Eq (skS.0 1 a) (skS.0 5 (skS.0 1 a) a_1) % 4.30/4.51 Clause #86 (by backward demodulation #[85, 83]): ∀ (a : Iota), Eq (property1 (skS.0 1 a) industrious pos) True % 4.30/4.51 Clause #89 (by clausification #[74]): Eq (∀ (E : Iota), And (grocer E) (property1 E industrious pos) → Exists fun F => And (property1 F honest pos) (Eq E F)) % 4.30/4.51 True % 4.30/4.51 Clause #90 (by clausification #[74]): Eq % 4.30/4.51 (And % 4.30/4.51 (∀ (A : Iota), % 4.30/4.51 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.30/4.51 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.30/4.51 (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D)))) % 4.30/4.51 True % 4.30/4.51 Clause #91 (by clausification #[89]): ∀ (a : Iota), % 4.30/4.51 Eq (And (grocer a) (property1 a industrious pos) → Exists fun F => And (property1 F honest pos) (Eq a F)) True % 4.30/4.51 Clause #92 (by clausification #[91]): ∀ (a : Iota), % 4.30/4.51 Or (Eq (And (grocer a) (property1 a industrious pos)) False) % 4.30/4.51 (Eq (Exists fun F => And (property1 F honest pos) (Eq a F)) True) % 4.30/4.51 Clause #93 (by clausification #[92]): ∀ (a : Iota), % 4.30/4.51 Or (Eq (Exists fun F => And (property1 F honest pos) (Eq a F)) True) % 4.30/4.51 (Or (Eq (grocer a) False) (Eq (property1 a industrious pos) False)) % 4.30/4.51 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), % 4.30/4.51 Or (Eq (grocer a) False) % 4.30/4.51 (Or (Eq (property1 a industrious pos) False) % 4.30/4.51 (Eq (And (property1 (skS.0 6 a a_1) honest pos) (Eq a (skS.0 6 a a_1))) True)) % 4.30/4.51 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), % 4.30/4.51 Or (Eq (grocer a) False) (Or (Eq (property1 a industrious pos) False) (Eq (Eq a (skS.0 6 a a_1)) True)) % 4.30/4.51 Clause #96 (by clausification #[94]): ∀ (a a_1 : Iota), % 4.30/4.51 Or (Eq (grocer a) False) % 4.30/4.51 (Or (Eq (property1 a industrious pos) False) (Eq (property1 (skS.0 6 a a_1) honest pos) True)) % 4.30/4.51 Clause #97 (by clausification #[95]): ∀ (a a_1 : Iota), Or (Eq (grocer a) False) (Or (Eq (property1 a industrious pos) False) (Eq a (skS.0 6 a a_1))) % 4.30/4.51 Clause #98 (by superposition #[97, 14]): ∀ (a a_1 : Iota), % 4.30/4.51 Or (Eq (property1 (skS.0 1 a) industrious pos) False) (Or (Eq (skS.0 1 a) (skS.0 6 (skS.0 1 a) a_1)) (Eq False True)) % 4.30/4.51 Clause #99 (by superposition #[96, 14]): ∀ (a a_1 : Iota), % 4.30/4.51 Or (Eq (property1 (skS.0 1 a) industrious pos) False) % 4.30/4.51 (Or (Eq (property1 (skS.0 6 (skS.0 1 a) a_1) honest pos) True) (Eq False True)) % 4.30/4.51 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota), % 4.30/4.51 Or (Eq (property1 (skS.0 1 a) industrious pos) False) (Eq (property1 (skS.0 6 (skS.0 1 a) a_1) honest pos) True) % 4.30/4.51 Clause #101 (by forward demodulation #[100, 86]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (property1 (skS.0 6 (skS.0 1 a) a_1) honest pos) True) % 4.30/4.51 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota), Eq (property1 (skS.0 6 (skS.0 1 a) a_1) honest pos) True % 4.30/4.51 Clause #103 (by clausification #[98]): ∀ (a a_1 : Iota), Or (Eq (property1 (skS.0 1 a) industrious pos) False) (Eq (skS.0 1 a) (skS.0 6 (skS.0 1 a) a_1)) % 4.37/4.54 Clause #104 (by forward demodulation #[103, 86]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 1 a) (skS.0 6 (skS.0 1 a) a_1)) % 4.37/4.54 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (skS.0 1 a) (skS.0 6 (skS.0 1 a) a_1) % 4.37/4.54 Clause #106 (by backward demodulation #[105, 102]): ∀ (a : Iota), Eq (property1 (skS.0 1 a) honest pos) True % 4.37/4.54 Clause #107 (by clausification #[90]): Eq (∀ (C : Iota), grocer C → Not (Exists fun D => And (property1 D healthy pos) (Eq C D))) True % 4.37/4.54 Clause #108 (by clausification #[90]): Eq % 4.37/4.54 (∀ (A : Iota), % 4.37/4.54 And (And (person A) (property1 A honest pos)) (property1 A industrious pos) → % 4.37/4.54 Exists fun B => And (property1 B healthy pos) (Eq A B)) % 4.37/4.54 True % 4.37/4.54 Clause #109 (by clausification #[107]): ∀ (a : Iota), Eq (grocer a → Not (Exists fun D => And (property1 D healthy pos) (Eq a D))) True % 4.37/4.54 Clause #110 (by clausification #[109]): ∀ (a : Iota), Or (Eq (grocer a) False) (Eq (Not (Exists fun D => And (property1 D healthy pos) (Eq a D))) True) % 4.37/4.54 Clause #111 (by clausification #[110]): ∀ (a : Iota), Or (Eq (grocer a) False) (Eq (Exists fun D => And (property1 D healthy pos) (Eq a D)) False) % 4.37/4.54 Clause #112 (by clausification #[111]): ∀ (a a_1 : Iota), Or (Eq (grocer a) False) (Eq (And (property1 a_1 healthy pos) (Eq a a_1)) False) % 4.37/4.54 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota), Or (Eq (grocer a) False) (Or (Eq (property1 a_1 healthy pos) False) (Eq (Eq a a_1) False)) % 4.37/4.54 Clause #114 (by clausification #[113]): ∀ (a a_1 : Iota), Or (Eq (grocer a) False) (Or (Eq (property1 a_1 healthy pos) False) (Ne a a_1)) % 4.37/4.54 Clause #115 (by destructive equality resolution #[114]): ∀ (a : Iota), Or (Eq (grocer a) False) (Eq (property1 a healthy pos) False) % 4.37/4.54 Clause #116 (by superposition #[115, 14]): ∀ (a : Iota), Or (Eq (property1 (skS.0 1 a) healthy pos) False) (Eq False True) % 4.37/4.54 Clause #119 (by clausification #[116]): ∀ (a : Iota), Eq (property1 (skS.0 1 a) healthy pos) False % 4.37/4.54 Clause #121 (by clausification #[108]): ∀ (a : Iota), % 4.37/4.54 Eq % 4.37/4.54 (And (And (person a) (property1 a honest pos)) (property1 a industrious pos) → % 4.37/4.54 Exists fun B => And (property1 B healthy pos) (Eq a B)) % 4.37/4.54 True % 4.37/4.54 Clause #122 (by clausification #[121]): ∀ (a : Iota), % 4.37/4.54 Or (Eq (And (And (person a) (property1 a honest pos)) (property1 a industrious pos)) False) % 4.37/4.54 (Eq (Exists fun B => And (property1 B healthy pos) (Eq a B)) True) % 4.37/4.54 Clause #123 (by clausification #[122]): ∀ (a : Iota), % 4.37/4.54 Or (Eq (Exists fun B => And (property1 B healthy pos) (Eq a B)) True) % 4.37/4.54 (Or (Eq (And (person a) (property1 a honest pos)) False) (Eq (property1 a industrious pos) False)) % 4.37/4.54 Clause #124 (by clausification #[123]): ∀ (a a_1 : Iota), % 4.37/4.54 Or (Eq (And (person a) (property1 a honest pos)) False) % 4.37/4.54 (Or (Eq (property1 a industrious pos) False) % 4.37/4.54 (Eq (And (property1 (skS.0 7 a a_1) healthy pos) (Eq a (skS.0 7 a a_1))) True)) % 4.37/4.54 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), % 4.37/4.54 Or (Eq (property1 a industrious pos) False) % 4.37/4.54 (Or (Eq (And (property1 (skS.0 7 a a_1) healthy pos) (Eq a (skS.0 7 a a_1))) True) % 4.37/4.54 (Or (Eq (person a) False) (Eq (property1 a honest pos) False))) % 4.37/4.54 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), % 4.37/4.54 Or (Eq (property1 a industrious pos) False) % 4.37/4.54 (Or (Eq (person a) False) (Or (Eq (property1 a honest pos) False) (Eq (Eq a (skS.0 7 a a_1)) True))) % 4.37/4.54 Clause #127 (by clausification #[125]): ∀ (a a_1 : Iota), % 4.37/4.54 Or (Eq (property1 a industrious pos) False) % 4.37/4.54 (Or (Eq (person a) False) % 4.37/4.54 (Or (Eq (property1 a honest pos) False) (Eq (property1 (skS.0 7 a a_1) healthy pos) True))) % 4.37/4.54 Clause #128 (by clausification #[126]): ∀ (a a_1 : Iota), % 4.37/4.54 Or (Eq (property1 a industrious pos) False) % 4.37/4.54 (Or (Eq (person a) False) (Or (Eq (property1 a honest pos) False) (Eq a (skS.0 7 a a_1)))) % 4.37/4.54 Clause #129 (by superposition #[128, 86]): ∀ (a a_1 : Iota), % 4.37/4.54 Or (Eq (person (skS.0 1 a)) False) % 4.37/4.54 (Or (Eq (property1 (skS.0 1 a) honest pos) False) (Or (Eq (skS.0 1 a) (skS.0 7 (skS.0 1 a) a_1)) (Eq False True))) % 4.37/4.54 Clause #130 (by superposition #[127, 86]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq (person (skS.0 1 a)) False) % 4.37/4.55 (Or (Eq (property1 (skS.0 1 a) honest pos) False) % 4.37/4.55 (Or (Eq (property1 (skS.0 7 (skS.0 1 a) a_1) healthy pos) True) (Eq False True))) % 4.37/4.55 Clause #131 (by clausification #[130]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq (person (skS.0 1 a)) False) % 4.37/4.55 (Or (Eq (property1 (skS.0 1 a) honest pos) False) (Eq (property1 (skS.0 7 (skS.0 1 a) a_1) healthy pos) True)) % 4.37/4.55 Clause #132 (by forward demodulation #[131, 37]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq True False) % 4.37/4.55 (Or (Eq (property1 (skS.0 1 a) honest pos) False) (Eq (property1 (skS.0 7 (skS.0 1 a) a_1) healthy pos) True)) % 4.37/4.55 Clause #133 (by clausification #[132]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq (property1 (skS.0 1 a) honest pos) False) (Eq (property1 (skS.0 7 (skS.0 1 a) a_1) healthy pos) True) % 4.37/4.55 Clause #134 (by forward demodulation #[133, 106]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (property1 (skS.0 7 (skS.0 1 a) a_1) healthy pos) True) % 4.37/4.55 Clause #135 (by clausification #[134]): ∀ (a a_1 : Iota), Eq (property1 (skS.0 7 (skS.0 1 a) a_1) healthy pos) True % 4.37/4.55 Clause #136 (by clausification #[129]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq (person (skS.0 1 a)) False) % 4.37/4.55 (Or (Eq (property1 (skS.0 1 a) honest pos) False) (Eq (skS.0 1 a) (skS.0 7 (skS.0 1 a) a_1))) % 4.37/4.55 Clause #137 (by forward demodulation #[136, 37]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq True False) (Or (Eq (property1 (skS.0 1 a) honest pos) False) (Eq (skS.0 1 a) (skS.0 7 (skS.0 1 a) a_1))) % 4.37/4.55 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota), Or (Eq (property1 (skS.0 1 a) honest pos) False) (Eq (skS.0 1 a) (skS.0 7 (skS.0 1 a) a_1)) % 4.37/4.55 Clause #139 (by forward demodulation #[138, 106]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 1 a) (skS.0 7 (skS.0 1 a) a_1)) % 4.37/4.55 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), Eq (skS.0 1 a) (skS.0 7 (skS.0 1 a) a_1) % 4.37/4.55 Clause #141 (by backward demodulation #[140, 135]): ∀ (a : Iota), Eq (property1 (skS.0 1 a) healthy pos) True % 4.37/4.55 Clause #142 (by superposition #[141, 119]): Eq True False % 4.37/4.55 Clause #143 (by clausification #[142]): False % 4.37/4.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------