TSTP Solution File: SWB029+2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SWB029+2 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 20:04:09 EDT 2023
% Result : Theorem 7.68s 8.01s
% Output : Proof 8.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWB029+2 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 06:39:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 7.68/8.01 SZS status Theorem for theBenchmark.p
% 7.68/8.01 SZS output start Proof for theBenchmark.p
% 7.68/8.01 Clause #0 (by assumption #[]): Eq (∀ (X C : Iota), Iff (iext uri_rdf_type X C) (icext C X)) True
% 7.68/8.01 Clause #1 (by assumption #[]): Eq
% 7.68/8.01 (∀ (Z C : Iota),
% 7.68/8.01 iext uri_owl_complementOf Z C → And (And (ic Z) (ic C)) (∀ (X : Iota), Iff (icext Z X) (Not (icext C X))))
% 7.68/8.01 True
% 7.68/8.01 Clause #2 (by assumption #[]): Eq
% 7.68/8.01 (∀ (Z S1 C1 S2 C2 : Iota),
% 7.68/8.01 And (And (And (iext uri_rdf_first S1 C1) (iext uri_rdf_rest S1 S2)) (iext uri_rdf_first S2 C2))
% 7.68/8.01 (iext uri_rdf_rest S2 uri_rdf_nil) →
% 7.68/8.01 Iff (iext uri_owl_intersectionOf Z S1)
% 7.68/8.01 (And (And (And (ic Z) (ic C1)) (ic C2)) (∀ (X : Iota), Iff (icext Z X) (And (icext C1 X) (icext C2 X)))))
% 7.68/8.01 True
% 7.68/8.01 Clause #4 (by assumption #[]): Eq
% 7.68/8.01 (Exists fun BNODE_x =>
% 7.68/8.01 Exists fun BNODE_y =>
% 7.68/8.01 Exists fun BNODE_l1 =>
% 7.68/8.01 Exists fun BNODE_l2 =>
% 7.68/8.01 And
% 7.68/8.01 (And
% 7.68/8.01 (And
% 7.68/8.01 (And
% 7.68/8.01 (And
% 7.68/8.01 (And
% 7.68/8.01 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.68/8.01 (iext uri_rdf_type uri_ex_w BNODE_x))
% 7.68/8.01 (iext uri_owl_intersectionOf BNODE_x BNODE_l1))
% 7.68/8.01 (iext uri_rdf_first BNODE_l1 uri_ex_A))
% 7.68/8.01 (iext uri_rdf_rest BNODE_l1 BNODE_l2))
% 7.68/8.01 (iext uri_rdf_first BNODE_l2 BNODE_y))
% 7.68/8.01 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil))
% 7.68/8.01 (iext uri_owl_complementOf BNODE_y uri_ex_A))
% 7.68/8.01 True
% 7.68/8.01 Clause #6 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (iext uri_rdf_type a C) (icext C a)) True
% 7.68/8.01 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Iff (iext uri_rdf_type a a_1) (icext a_1 a)) True
% 7.68/8.01 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (iext uri_rdf_type a a_1) False) (Eq (icext a_1 a) True)
% 7.68/8.01 Clause #10 (by clausification #[1]): ∀ (a : Iota),
% 7.68/8.01 Eq
% 7.68/8.01 (∀ (C : Iota),
% 7.68/8.01 iext uri_owl_complementOf a C → And (And (ic a) (ic C)) (∀ (X : Iota), Iff (icext a X) (Not (icext C X))))
% 7.68/8.01 True
% 7.68/8.01 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota),
% 7.68/8.01 Eq (iext uri_owl_complementOf a a_1 → And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (Not (icext a_1 X))))
% 7.68/8.01 True
% 7.68/8.01 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota),
% 7.68/8.01 Or (Eq (iext uri_owl_complementOf a a_1) False)
% 7.68/8.01 (Eq (And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (Not (icext a_1 X)))) True)
% 7.68/8.01 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota),
% 7.68/8.01 Or (Eq (iext uri_owl_complementOf a a_1) False) (Eq (∀ (X : Iota), Iff (icext a X) (Not (icext a_1 X))) True)
% 7.68/8.01 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota),
% 7.68/8.01 Or (Eq (iext uri_owl_complementOf a a_1) False) (Eq (Iff (icext a a_2) (Not (icext a_1 a_2))) True)
% 7.68/8.01 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota),
% 7.68/8.01 Or (Eq (iext uri_owl_complementOf a a_1) False) (Or (Eq (icext a a_2) False) (Eq (Not (icext a_1 a_2)) True))
% 7.68/8.01 Clause #21 (by clausification #[2]): ∀ (a : Iota),
% 7.68/8.01 Eq
% 7.68/8.01 (∀ (S1 C1 S2 C2 : Iota),
% 7.68/8.01 And (And (And (iext uri_rdf_first S1 C1) (iext uri_rdf_rest S1 S2)) (iext uri_rdf_first S2 C2))
% 7.68/8.01 (iext uri_rdf_rest S2 uri_rdf_nil) →
% 7.68/8.01 Iff (iext uri_owl_intersectionOf a S1)
% 7.68/8.01 (And (And (And (ic a) (ic C1)) (ic C2)) (∀ (X : Iota), Iff (icext a X) (And (icext C1 X) (icext C2 X)))))
% 7.68/8.01 True
% 7.68/8.01 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota),
% 7.68/8.01 Eq
% 7.68/8.01 (∀ (C1 S2 C2 : Iota),
% 7.68/8.01 And (And (And (iext uri_rdf_first a C1) (iext uri_rdf_rest a S2)) (iext uri_rdf_first S2 C2))
% 7.68/8.01 (iext uri_rdf_rest S2 uri_rdf_nil) →
% 7.68/8.01 Iff (iext uri_owl_intersectionOf a_1 a)
% 7.68/8.01 (And (And (And (ic a_1) (ic C1)) (ic C2)) (∀ (X : Iota), Iff (icext a_1 X) (And (icext C1 X) (icext C2 X)))))
% 7.68/8.01 True
% 7.68/8.01 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 7.68/8.01 Eq
% 7.68/8.01 (∀ (S2 C2 : Iota),
% 7.68/8.01 And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a S2)) (iext uri_rdf_first S2 C2))
% 7.68/8.01 (iext uri_rdf_rest S2 uri_rdf_nil) →
% 7.68/8.01 Iff (iext uri_owl_intersectionOf a_2 a)
% 7.83/8.05 (And (And (And (ic a_2) (ic a_1)) (ic C2))
% 7.83/8.05 (∀ (X : Iota), Iff (icext a_2 X) (And (icext a_1 X) (icext C2 X)))))
% 7.83/8.05 True
% 7.83/8.05 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.83/8.05 Eq
% 7.83/8.05 (∀ (C2 : Iota),
% 7.83/8.05 And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 C2))
% 7.83/8.05 (iext uri_rdf_rest a_2 uri_rdf_nil) →
% 7.83/8.05 Iff (iext uri_owl_intersectionOf a_3 a)
% 7.83/8.05 (And (And (And (ic a_3) (ic a_1)) (ic C2))
% 7.83/8.05 (∀ (X : Iota), Iff (icext a_3 X) (And (icext a_1 X) (icext C2 X)))))
% 7.83/8.05 True
% 7.83/8.05 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.83/8.05 Eq
% 7.83/8.05 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3))
% 7.83/8.05 (iext uri_rdf_rest a_2 uri_rdf_nil) →
% 7.83/8.05 Iff (iext uri_owl_intersectionOf a_4 a)
% 7.83/8.05 (And (And (And (ic a_4) (ic a_1)) (ic a_3))
% 7.83/8.05 (∀ (X : Iota), Iff (icext a_4 X) (And (icext a_1 X) (icext a_3 X)))))
% 7.83/8.05 True
% 7.83/8.05 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.83/8.05 Or
% 7.83/8.05 (Eq
% 7.83/8.05 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3))
% 7.83/8.05 (iext uri_rdf_rest a_2 uri_rdf_nil))
% 7.83/8.05 False)
% 7.83/8.05 (Eq
% 7.83/8.05 (Iff (iext uri_owl_intersectionOf a_4 a)
% 7.83/8.05 (And (And (And (ic a_4) (ic a_1)) (ic a_3))
% 7.83/8.05 (∀ (X : Iota), Iff (icext a_4 X) (And (icext a_1 X) (icext a_3 X)))))
% 7.83/8.05 True)
% 7.83/8.05 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.83/8.05 Or
% 7.83/8.05 (Eq
% 7.83/8.05 (Iff (iext uri_owl_intersectionOf a a_1)
% 7.83/8.05 (And (And (And (ic a) (ic a_2)) (ic a_3)) (∀ (X : Iota), Iff (icext a X) (And (icext a_2 X) (icext a_3 X)))))
% 7.83/8.05 True)
% 7.83/8.05 (Or (Eq (And (And (iext uri_rdf_first a_1 a_2) (iext uri_rdf_rest a_1 a_4)) (iext uri_rdf_first a_4 a_3)) False)
% 7.83/8.05 (Eq (iext uri_rdf_rest a_4 uri_rdf_nil) False))
% 7.83/8.05 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.83/8.05 Or (Eq (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3)) False)
% 7.83/8.05 (Or (Eq (iext uri_rdf_rest a_2 uri_rdf_nil) False)
% 7.83/8.05 (Or (Eq (iext uri_owl_intersectionOf a_4 a) False)
% 7.83/8.05 (Eq
% 7.83/8.05 (And (And (And (ic a_4) (ic a_1)) (ic a_3))
% 7.83/8.05 (∀ (X : Iota), Iff (icext a_4 X) (And (icext a_1 X) (icext a_3 X))))
% 7.83/8.05 True)))
% 7.83/8.05 Clause #40 (by clausification #[17]): ∀ (a a_1 a_2 : Iota),
% 7.83/8.05 Or (Eq (iext uri_owl_complementOf a a_1) False) (Or (Eq (icext a a_2) False) (Eq (icext a_1 a_2) False))
% 7.83/8.05 Clause #41 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.83/8.05 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 7.83/8.05 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False)
% 7.83/8.05 (Or
% 7.83/8.05 (Eq
% 7.83/8.05 (And (And (And (ic a_1) (ic a_3)) (ic a_4))
% 7.83/8.05 (∀ (X : Iota), Iff (icext a_1 X) (And (icext a_3 X) (icext a_4 X))))
% 7.83/8.05 True)
% 7.83/8.05 (Or (Eq (And (iext uri_rdf_first a_2 a_3) (iext uri_rdf_rest a_2 a)) False)
% 7.83/8.05 (Eq (iext uri_rdf_first a a_4) False))))
% 7.83/8.05 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.83/8.05 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 7.83/8.05 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False)
% 7.83/8.05 (Or (Eq (And (iext uri_rdf_first a_2 a_3) (iext uri_rdf_rest a_2 a)) False)
% 7.83/8.05 (Or (Eq (iext uri_rdf_first a a_4) False)
% 7.83/8.05 (Eq (∀ (X : Iota), Iff (icext a_1 X) (And (icext a_3 X) (icext a_4 X))) True))))
% 7.83/8.05 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.83/8.05 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 7.83/8.05 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False)
% 7.83/8.05 (Or (Eq (iext uri_rdf_first a a_3) False)
% 7.83/8.05 (Or (Eq (∀ (X : Iota), Iff (icext a_1 X) (And (icext a_4 X) (icext a_3 X))) True)
% 7.83/8.05 (Or (Eq (iext uri_rdf_first a_2 a_4) False) (Eq (iext uri_rdf_rest a_2 a) False)))))
% 7.83/8.05 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.83/8.05 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 7.83/8.05 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False)
% 7.83/8.05 (Or (Eq (iext uri_rdf_first a a_3) False)
% 7.83/8.05 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 7.90/8.09 (Or (Eq (iext uri_rdf_rest a_2 a) False)
% 7.90/8.09 (Eq (Iff (icext a_1 a_5) (And (icext a_4 a_5) (icext a_3 a_5))) True)))))
% 7.90/8.09 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.90/8.09 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 7.90/8.09 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False)
% 7.90/8.09 (Or (Eq (iext uri_rdf_first a a_3) False)
% 7.90/8.09 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 7.90/8.09 (Or (Eq (iext uri_rdf_rest a_2 a) False)
% 7.90/8.09 (Or (Eq (icext a_1 a_5) False) (Eq (And (icext a_4 a_5) (icext a_3 a_5)) True))))))
% 7.90/8.09 Clause #54 (by clausification #[4]): ∀ (a : Iota),
% 7.90/8.09 Eq
% 7.90/8.09 (Exists fun BNODE_y =>
% 7.90/8.09 Exists fun BNODE_l1 =>
% 7.90/8.09 Exists fun BNODE_l2 =>
% 7.90/8.09 And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.90/8.09 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.90/8.09 (iext uri_owl_intersectionOf (skS.0 1 a) BNODE_l1))
% 7.90/8.09 (iext uri_rdf_first BNODE_l1 uri_ex_A))
% 7.90/8.09 (iext uri_rdf_rest BNODE_l1 BNODE_l2))
% 7.90/8.09 (iext uri_rdf_first BNODE_l2 BNODE_y))
% 7.90/8.09 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil))
% 7.90/8.09 (iext uri_owl_complementOf BNODE_y uri_ex_A))
% 7.90/8.09 True
% 7.90/8.09 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota),
% 7.90/8.09 Eq
% 7.90/8.09 (Exists fun BNODE_l1 =>
% 7.90/8.09 Exists fun BNODE_l2 =>
% 7.90/8.09 And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.90/8.09 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.90/8.09 (iext uri_owl_intersectionOf (skS.0 1 a) BNODE_l1))
% 7.90/8.09 (iext uri_rdf_first BNODE_l1 uri_ex_A))
% 7.90/8.09 (iext uri_rdf_rest BNODE_l1 BNODE_l2))
% 7.90/8.09 (iext uri_rdf_first BNODE_l2 (skS.0 2 a a_1)))
% 7.90/8.09 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil))
% 7.90/8.09 (iext uri_owl_complementOf (skS.0 2 a a_1) uri_ex_A))
% 7.90/8.09 True
% 7.90/8.09 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 7.90/8.09 Eq
% 7.90/8.09 (Exists fun BNODE_l2 =>
% 7.90/8.09 And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.90/8.09 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.90/8.09 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)))
% 7.90/8.09 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A))
% 7.90/8.09 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) BNODE_l2))
% 7.90/8.09 (iext uri_rdf_first BNODE_l2 (skS.0 2 a a_1)))
% 7.90/8.09 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil))
% 7.90/8.09 (iext uri_owl_complementOf (skS.0 2 a a_1) uri_ex_A))
% 7.90/8.09 True
% 7.90/8.09 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.90/8.09 Eq
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.90/8.09 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.90/8.09 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)))
% 7.90/8.09 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A))
% 7.90/8.09 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)))
% 7.90/8.09 (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) (skS.0 2 a a_1)))
% 7.90/8.09 (iext uri_rdf_rest (skS.0 4 a a_1 a_2 a_3) uri_rdf_nil))
% 7.90/8.09 (iext uri_owl_complementOf (skS.0 2 a a_1) uri_ex_A))
% 7.90/8.09 True
% 7.90/8.09 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (iext uri_owl_complementOf (skS.0 2 a a_1) uri_ex_A) True
% 7.90/8.09 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.90/8.09 Eq
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And
% 7.90/8.09 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.90/8.09 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.90/8.13 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)))
% 7.90/8.13 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A))
% 7.90/8.13 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)))
% 7.90/8.13 (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) (skS.0 2 a a_1)))
% 7.90/8.13 (iext uri_rdf_rest (skS.0 4 a a_1 a_2 a_3) uri_rdf_nil))
% 7.90/8.13 True
% 7.90/8.13 Clause #63 (by superposition #[58, 40]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (icext (skS.0 2 a a_1) a_2) False) (Eq (icext uri_ex_A a_2) False))
% 7.90/8.13 Clause #66 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), Or (Eq (icext (skS.0 2 a a_1) a_2) False) (Eq (icext uri_ex_A a_2) False)
% 7.90/8.13 Clause #76 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.90/8.13 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 7.90/8.13 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first a a_3) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_rest a_2 a) False) (Or (Eq (icext a_1 a_5) False) (Eq (icext a_3 a_5) True))))))
% 7.90/8.13 Clause #77 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.90/8.13 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 7.90/8.13 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first a a_3) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_rest a_2 a) False) (Or (Eq (icext a_1 a_5) False) (Eq (icext a_4 a_5) True))))))
% 7.90/8.13 Clause #78 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_rest (skS.0 4 a a_1 a_2 a_3) uri_rdf_nil) True
% 7.90/8.13 Clause #79 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.90/8.13 Eq
% 7.90/8.13 (And
% 7.90/8.13 (And
% 7.90/8.13 (And
% 7.90/8.13 (And
% 7.90/8.13 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.90/8.13 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.90/8.13 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)))
% 7.90/8.13 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A))
% 7.90/8.13 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)))
% 7.90/8.13 (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) (skS.0 2 a a_1)))
% 7.90/8.13 True
% 7.90/8.13 Clause #86 (by superposition #[78, 76]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 7.90/8.13 Or (Eq True False)
% 7.90/8.13 (Or (Eq (iext uri_owl_intersectionOf a a_1) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first (skS.0 4 a_2 a_3 a_4 a_5) a_6) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first a_1 a_7) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 4 a_2 a_3 a_4 a_5)) False)
% 7.90/8.13 (Or (Eq (icext a a_8) False) (Eq (icext a_6 a_8) True))))))
% 7.90/8.13 Clause #87 (by superposition #[78, 77]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 7.90/8.13 Or (Eq True False)
% 7.90/8.13 (Or (Eq (iext uri_owl_intersectionOf a a_1) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first (skS.0 4 a_2 a_3 a_4 a_5) a_6) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first a_1 a_7) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 4 a_2 a_3 a_4 a_5)) False)
% 7.90/8.13 (Or (Eq (icext a a_8) False) (Eq (icext a_7 a_8) True))))))
% 7.90/8.13 Clause #91 (by clausification #[87]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 7.90/8.13 Or (Eq (iext uri_owl_intersectionOf a a_1) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first (skS.0 4 a_2 a_3 a_4 a_5) a_6) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first a_1 a_7) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 4 a_2 a_3 a_4 a_5)) False)
% 7.90/8.13 (Or (Eq (icext a a_8) False) (Eq (icext a_7 a_8) True)))))
% 7.90/8.13 Clause #92 (by clausification #[86]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 7.90/8.13 Or (Eq (iext uri_owl_intersectionOf a a_1) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first (skS.0 4 a_2 a_3 a_4 a_5) a_6) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_first a_1 a_7) False)
% 7.90/8.13 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 4 a_2 a_3 a_4 a_5)) False)
% 7.90/8.13 (Or (Eq (icext a a_8) False) (Eq (icext a_6 a_8) True)))))
% 7.90/8.13 Clause #98 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) (skS.0 2 a a_1)) True
% 7.90/8.13 Clause #99 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.90/8.13 Eq
% 7.90/8.13 (And
% 7.90/8.13 (And
% 7.90/8.13 (And
% 7.90/8.13 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.99/8.18 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.99/8.18 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)))
% 7.99/8.18 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A))
% 7.99/8.18 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)))
% 7.99/8.18 True
% 7.99/8.18 Clause #103 (by clausification #[99]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)) True
% 7.99/8.18 Clause #104 (by clausification #[99]): ∀ (a a_1 a_2 : Iota),
% 7.99/8.18 Eq
% 7.99/8.18 (And
% 7.99/8.18 (And
% 7.99/8.18 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.99/8.18 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.99/8.18 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)))
% 7.99/8.18 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A))
% 7.99/8.18 True
% 7.99/8.18 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A) True
% 7.99/8.18 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 : Iota),
% 7.99/8.18 Eq
% 7.99/8.18 (And
% 7.99/8.18 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.99/8.18 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.99/8.18 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)))
% 7.99/8.18 True
% 7.99/8.18 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)) True
% 7.99/8.18 Clause #108 (by clausification #[106]): ∀ (a : Iota),
% 7.99/8.18 Eq
% 7.99/8.18 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class))
% 7.99/8.18 (iext uri_rdf_type uri_ex_w (skS.0 1 a)))
% 7.99/8.18 True
% 7.99/8.18 Clause #112 (by superposition #[107, 91]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota),
% 7.99/8.18 Or (Eq True False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) a_4) False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_first (skS.0 3 a_5 a_6 a_7) a_8) False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_rest (skS.0 3 a_5 a_6 a_7) (skS.0 4 a a_1 a_2 a_3)) False)
% 7.99/8.18 (Or (Eq (icext (skS.0 1 a_5) a_9) False) (Eq (icext a_8 a_9) True)))))
% 7.99/8.18 Clause #113 (by superposition #[107, 92]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota),
% 7.99/8.18 Or (Eq True False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) a_4) False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_first (skS.0 3 a_5 a_6 a_7) a_8) False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_rest (skS.0 3 a_5 a_6 a_7) (skS.0 4 a a_1 a_2 a_3)) False)
% 7.99/8.18 (Or (Eq (icext (skS.0 1 a_5) a_9) False) (Eq (icext a_4 a_9) True)))))
% 7.99/8.18 Clause #115 (by clausification #[108]): ∀ (a : Iota), Eq (iext uri_rdf_type uri_ex_w (skS.0 1 a)) True
% 7.99/8.18 Clause #117 (by superposition #[115, 9]): ∀ (a : Iota), Or (Eq True False) (Eq (icext (skS.0 1 a) uri_ex_w) True)
% 7.99/8.18 Clause #131 (by clausification #[117]): ∀ (a : Iota), Eq (icext (skS.0 1 a) uri_ex_w) True
% 7.99/8.18 Clause #160 (by clausification #[112]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota),
% 7.99/8.18 Or (Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) a_4) False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_first (skS.0 3 a_5 a_6 a_7) a_8) False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_rest (skS.0 3 a_5 a_6 a_7) (skS.0 4 a a_1 a_2 a_3)) False)
% 7.99/8.18 (Or (Eq (icext (skS.0 1 a_5) a_9) False) (Eq (icext a_8 a_9) True))))
% 7.99/8.18 Clause #161 (by superposition #[160, 98]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 7.99/8.18 Or (Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) a_3) False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_4 a_5 a_6 a_7)) False)
% 7.99/8.18 (Or (Eq (icext (skS.0 1 a) a_8) False) (Or (Eq (icext a_3 a_8) True) (Eq False True))))
% 7.99/8.18 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 7.99/8.18 Or (Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) a_3) False)
% 7.99/8.18 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_4 a_5 a_6 a_7)) False)
% 7.99/8.18 (Or (Eq (icext (skS.0 1 a) a_8) False) (Eq (icext a_3 a_8) True)))
% 7.99/8.18 Clause #163 (by superposition #[162, 105]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 7.99/8.18 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_3 a_4 a_5 a_6)) False)
% 7.99/8.18 (Or (Eq (icext (skS.0 1 a) a_7) False) (Or (Eq (icext uri_ex_A a_7) True) (Eq False True)))
% 8.02/8.22 Clause #164 (by clausification #[163]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 8.02/8.22 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_3 a_4 a_5 a_6)) False)
% 8.02/8.22 (Or (Eq (icext (skS.0 1 a) a_7) False) (Eq (icext uri_ex_A a_7) True))
% 8.02/8.22 Clause #165 (by superposition #[164, 103]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 1 a) a_1) False) (Or (Eq (icext uri_ex_A a_1) True) (Eq False True))
% 8.02/8.22 Clause #166 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 1 a) a_1) False) (Eq (icext uri_ex_A a_1) True)
% 8.02/8.22 Clause #167 (by superposition #[166, 131]): Or (Eq (icext uri_ex_A uri_ex_w) True) (Eq False True)
% 8.02/8.22 Clause #168 (by clausification #[167]): Eq (icext uri_ex_A uri_ex_w) True
% 8.02/8.22 Clause #172 (by clausification #[113]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota),
% 8.02/8.22 Or (Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) a_4) False)
% 8.02/8.22 (Or (Eq (iext uri_rdf_first (skS.0 3 a_5 a_6 a_7) a_8) False)
% 8.02/8.22 (Or (Eq (iext uri_rdf_rest (skS.0 3 a_5 a_6 a_7) (skS.0 4 a a_1 a_2 a_3)) False)
% 8.02/8.22 (Or (Eq (icext (skS.0 1 a_5) a_9) False) (Eq (icext a_4 a_9) True))))
% 8.02/8.22 Clause #173 (by superposition #[172, 98]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 8.02/8.22 Or (Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) a_3) False)
% 8.02/8.22 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_4 a_5 a_6 a_7)) False)
% 8.02/8.22 (Or (Eq (icext (skS.0 1 a) a_8) False) (Or (Eq (icext (skS.0 2 a_4 a_5) a_8) True) (Eq False True))))
% 8.02/8.22 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 8.02/8.22 Or (Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) a_3) False)
% 8.02/8.22 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_4 a_5 a_6 a_7)) False)
% 8.02/8.22 (Or (Eq (icext (skS.0 1 a) a_8) False) (Eq (icext (skS.0 2 a_4 a_5) a_8) True)))
% 8.02/8.22 Clause #175 (by superposition #[174, 105]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 8.02/8.22 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_3 a_4 a_5 a_6)) False)
% 8.02/8.22 (Or (Eq (icext (skS.0 1 a) a_7) False) (Or (Eq (icext (skS.0 2 a_3 a_4) a_7) True) (Eq False True)))
% 8.02/8.22 Clause #176 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 8.02/8.22 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_3 a_4 a_5 a_6)) False)
% 8.02/8.22 (Or (Eq (icext (skS.0 1 a) a_7) False) (Eq (icext (skS.0 2 a_3 a_4) a_7) True))
% 8.02/8.22 Clause #177 (by superposition #[176, 103]): ∀ (a a_1 a_2 : Iota), Or (Eq (icext (skS.0 1 a) a_1) False) (Or (Eq (icext (skS.0 2 a a_2) a_1) True) (Eq False True))
% 8.02/8.22 Clause #178 (by clausification #[177]): ∀ (a a_1 a_2 : Iota), Or (Eq (icext (skS.0 1 a) a_1) False) (Eq (icext (skS.0 2 a a_2) a_1) True)
% 8.02/8.22 Clause #179 (by superposition #[178, 131]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 2 a a_1) uri_ex_w) True) (Eq False True)
% 8.02/8.22 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), Eq (icext (skS.0 2 a a_1) uri_ex_w) True
% 8.02/8.22 Clause #181 (by superposition #[180, 66]): Or (Eq True False) (Eq (icext uri_ex_A uri_ex_w) False)
% 8.02/8.22 Clause #185 (by clausification #[181]): Eq (icext uri_ex_A uri_ex_w) False
% 8.02/8.22 Clause #186 (by superposition #[185, 168]): Eq False True
% 8.02/8.22 Clause #187 (by clausification #[186]): False
% 8.02/8.22 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------