TSTP Solution File: LCL518+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL518+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n012.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 07:10:01 EDT 2023
% Result : Theorem 63.86s 64.01s
% Output : Proof 64.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL518+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : duper %s
% 0.17/0.36 % Computer : n012.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Thu Aug 24 19:31:41 EDT 2023
% 0.17/0.36 % CPUTime :
% 63.86/64.01 SZS status Theorem for theBenchmark.p
% 63.86/64.01 SZS output start Proof for theBenchmark.p
% 63.86/64.01 Clause #0 (by assumption #[]): Eq (Iff modus_ponens (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y)) True
% 63.86/64.01 Clause #1 (by assumption #[]): Eq (Iff substitution_of_equivalents (∀ (X Y : Iota), is_a_theorem (equiv X Y) → Eq X Y)) True
% 63.86/64.01 Clause #15 (by assumption #[]): Eq (Iff kn1 (∀ (P : Iota), is_a_theorem (implies P (and P P)))) True
% 63.86/64.01 Clause #16 (by assumption #[]): Eq (Iff kn2 (∀ (P Q : Iota), is_a_theorem (implies (and P Q) P))) True
% 63.86/64.01 Clause #17 (by assumption #[]): Eq (Iff kn3 (∀ (P Q R : Iota), is_a_theorem (implies (implies P Q) (implies (not (and Q R)) (not (and R P)))))) True
% 63.86/64.01 Clause #21 (by assumption #[]): Eq (Iff r1 (∀ (P : Iota), is_a_theorem (implies (or P P) P))) True
% 63.86/64.01 Clause #26 (by assumption #[]): Eq (op_or → ∀ (X Y : Iota), Eq (or X Y) (not (and (not X) (not Y)))) True
% 63.86/64.01 Clause #27 (by assumption #[]): Eq (op_and → ∀ (X Y : Iota), Eq (and X Y) (not (or (not X) (not Y)))) True
% 63.86/64.01 Clause #28 (by assumption #[]): Eq (op_implies_and → ∀ (X Y : Iota), Eq (implies X Y) (not (and X (not Y)))) True
% 63.86/64.01 Clause #29 (by assumption #[]): Eq (op_implies_or → ∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True
% 63.86/64.01 Clause #30 (by assumption #[]): Eq (op_equiv → ∀ (X Y : Iota), Eq (equiv X Y) (and (implies X Y) (implies Y X))) True
% 63.86/64.01 Clause #31 (by assumption #[]): Eq op_or True
% 63.86/64.01 Clause #32 (by assumption #[]): Eq op_implies_and True
% 63.86/64.01 Clause #33 (by assumption #[]): Eq op_equiv True
% 63.86/64.01 Clause #34 (by assumption #[]): Eq modus_ponens True
% 63.86/64.01 Clause #35 (by assumption #[]): Eq kn1 True
% 63.86/64.01 Clause #36 (by assumption #[]): Eq kn2 True
% 63.86/64.01 Clause #37 (by assumption #[]): Eq kn3 True
% 63.86/64.01 Clause #38 (by assumption #[]): Eq substitution_of_equivalents True
% 63.86/64.01 Clause #39 (by assumption #[]): Eq op_implies_or True
% 63.86/64.01 Clause #40 (by assumption #[]): Eq op_and True
% 63.86/64.01 Clause #41 (by assumption #[]): Eq (Not r1) True
% 63.86/64.01 Clause #43 (by clausification #[0]): Or (Eq modus_ponens False)
% 63.86/64.01 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 63.86/64.01 Clause #54 (by clausification #[1]): Or (Eq substitution_of_equivalents False) (Eq (∀ (X Y : Iota), is_a_theorem (equiv X Y) → Eq X Y) True)
% 63.86/64.01 Clause #62 (by clausification #[41]): Eq r1 False
% 63.86/64.01 Clause #63 (by clausification #[43]): ∀ (a : Iota),
% 63.86/64.01 Or (Eq modus_ponens False)
% 63.86/64.01 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 63.86/64.01 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 63.86/64.01 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 63.86/64.01 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota),
% 63.86/64.01 Or (Eq modus_ponens False)
% 63.86/64.01 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 63.86/64.01 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota),
% 63.86/64.01 Or (Eq modus_ponens False)
% 63.86/64.01 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 63.86/64.01 Clause #67 (by forward demodulation #[66, 34]): ∀ (a a_1 : Iota),
% 63.86/64.01 Or (Eq True False)
% 63.86/64.01 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 63.86/64.01 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota),
% 63.86/64.01 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 63.86/64.01 Clause #69 (by clausification #[21]): Or (Eq r1 True) (Eq (∀ (P : Iota), is_a_theorem (implies (or P P) P)) False)
% 63.86/64.01 Clause #71 (by clausification #[69]): ∀ (a : Iota), Or (Eq r1 True) (Eq (Not (is_a_theorem (implies (or (skS.0 4 a) (skS.0 4 a)) (skS.0 4 a)))) True)
% 63.86/64.01 Clause #72 (by clausification #[71]): ∀ (a : Iota), Or (Eq r1 True) (Eq (is_a_theorem (implies (or (skS.0 4 a) (skS.0 4 a)) (skS.0 4 a))) False)
% 63.86/64.01 Clause #73 (by forward demodulation #[72, 62]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (implies (or (skS.0 4 a) (skS.0 4 a)) (skS.0 4 a))) False)
% 63.86/64.01 Clause #74 (by clausification #[73]): ∀ (a : Iota), Eq (is_a_theorem (implies (or (skS.0 4 a) (skS.0 4 a)) (skS.0 4 a))) False
% 63.86/64.03 Clause #78 (by clausification #[15]): Or (Eq kn1 False) (Eq (∀ (P : Iota), is_a_theorem (implies P (and P P))) True)
% 63.86/64.03 Clause #88 (by clausification #[78]): ∀ (a : Iota), Or (Eq kn1 False) (Eq (is_a_theorem (implies a (and a a))) True)
% 63.86/64.03 Clause #89 (by forward demodulation #[88, 35]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies a (and a a))) True)
% 63.86/64.03 Clause #90 (by clausification #[89]): ∀ (a : Iota), Eq (is_a_theorem (implies a (and a a))) True
% 63.86/64.03 Clause #91 (by superposition #[90, 68]): ∀ (a a_1 : Iota),
% 63.86/64.03 Or (Eq (is_a_theorem a) True) (Or (Eq True False) (Eq (is_a_theorem (implies (implies a_1 (and a_1 a_1)) a)) False))
% 63.86/64.03 Clause #92 (by clausification #[54]): ∀ (a : Iota), Or (Eq substitution_of_equivalents False) (Eq (∀ (Y : Iota), is_a_theorem (equiv a Y) → Eq a Y) True)
% 63.86/64.03 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), Or (Eq substitution_of_equivalents False) (Eq (is_a_theorem (equiv a a_1) → Eq a a_1) True)
% 63.86/64.03 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota),
% 63.86/64.03 Or (Eq substitution_of_equivalents False) (Or (Eq (is_a_theorem (equiv a a_1)) False) (Eq (Eq a a_1) True))
% 63.86/64.03 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Or (Eq substitution_of_equivalents False) (Or (Eq (is_a_theorem (equiv a a_1)) False) (Eq a a_1))
% 63.86/64.03 Clause #96 (by forward demodulation #[95, 38]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (is_a_theorem (equiv a a_1)) False) (Eq a a_1))
% 63.86/64.03 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (equiv a a_1)) False) (Eq a a_1)
% 63.86/64.03 Clause #114 (by clausification #[16]): Or (Eq kn2 False) (Eq (∀ (P Q : Iota), is_a_theorem (implies (and P Q) P)) True)
% 63.86/64.03 Clause #120 (by clausification #[114]): ∀ (a : Iota), Or (Eq kn2 False) (Eq (∀ (Q : Iota), is_a_theorem (implies (and a Q) a)) True)
% 63.86/64.03 Clause #121 (by clausification #[120]): ∀ (a a_1 : Iota), Or (Eq kn2 False) (Eq (is_a_theorem (implies (and a a_1) a)) True)
% 63.86/64.03 Clause #122 (by forward demodulation #[121, 36]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (and a a_1) a)) True)
% 63.86/64.03 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (and a a_1) a)) True
% 63.86/64.03 Clause #124 (by superposition #[123, 68]): ∀ (a a_1 a_2 : Iota),
% 63.86/64.03 Or (Eq (is_a_theorem a) True) (Or (Eq True False) (Eq (is_a_theorem (implies (implies (and a_1 a_2) a_1) a)) False))
% 63.86/64.03 Clause #214 (by clausification #[29]): Or (Eq op_implies_or False) (Eq (∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True)
% 63.86/64.03 Clause #215 (by clausification #[214]): ∀ (a : Iota), Or (Eq op_implies_or False) (Eq (∀ (Y : Iota), Eq (implies a Y) (or (not a) Y)) True)
% 63.86/64.03 Clause #216 (by clausification #[215]): ∀ (a a_1 : Iota), Or (Eq op_implies_or False) (Eq (Eq (implies a a_1) (or (not a) a_1)) True)
% 63.86/64.03 Clause #217 (by clausification #[216]): ∀ (a a_1 : Iota), Or (Eq op_implies_or False) (Eq (implies a a_1) (or (not a) a_1))
% 63.86/64.03 Clause #218 (by forward demodulation #[217, 39]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (implies a a_1) (or (not a) a_1))
% 63.86/64.03 Clause #219 (by clausification #[218]): ∀ (a a_1 : Iota), Eq (implies a a_1) (or (not a) a_1)
% 63.86/64.03 Clause #242 (by clausification #[28]): Or (Eq op_implies_and False) (Eq (∀ (X Y : Iota), Eq (implies X Y) (not (and X (not Y)))) True)
% 63.86/64.03 Clause #243 (by clausification #[242]): ∀ (a : Iota), Or (Eq op_implies_and False) (Eq (∀ (Y : Iota), Eq (implies a Y) (not (and a (not Y)))) True)
% 63.86/64.03 Clause #244 (by clausification #[243]): ∀ (a a_1 : Iota), Or (Eq op_implies_and False) (Eq (Eq (implies a a_1) (not (and a (not a_1)))) True)
% 63.86/64.03 Clause #245 (by clausification #[244]): ∀ (a a_1 : Iota), Or (Eq op_implies_and False) (Eq (implies a a_1) (not (and a (not a_1))))
% 63.86/64.03 Clause #246 (by forward demodulation #[245, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (implies a a_1) (not (and a (not a_1))))
% 63.86/64.03 Clause #247 (by clausification #[246]): ∀ (a a_1 : Iota), Eq (implies a a_1) (not (and a (not a_1)))
% 63.86/64.03 Clause #263 (by clausification #[17]): Or (Eq kn3 False)
% 63.86/64.03 (Eq (∀ (P Q R : Iota), is_a_theorem (implies (implies P Q) (implies (not (and Q R)) (not (and R P))))) True)
% 63.89/64.06 Clause #271 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies (and a_1 a_2) a_1) a)) False)
% 63.89/64.06 Clause #276 (by clausification #[91]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies a_1 (and a_1 a_1)) a)) False)
% 63.89/64.06 Clause #307 (by clausification #[27]): Or (Eq op_and False) (Eq (∀ (X Y : Iota), Eq (and X Y) (not (or (not X) (not Y)))) True)
% 63.89/64.06 Clause #308 (by clausification #[307]): ∀ (a : Iota), Or (Eq op_and False) (Eq (∀ (Y : Iota), Eq (and a Y) (not (or (not a) (not Y)))) True)
% 63.89/64.06 Clause #309 (by clausification #[308]): ∀ (a a_1 : Iota), Or (Eq op_and False) (Eq (Eq (and a a_1) (not (or (not a) (not a_1)))) True)
% 63.89/64.06 Clause #310 (by clausification #[309]): ∀ (a a_1 : Iota), Or (Eq op_and False) (Eq (and a a_1) (not (or (not a) (not a_1))))
% 63.89/64.06 Clause #311 (by forward demodulation #[310, 40]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (and a a_1) (not (or (not a) (not a_1))))
% 63.89/64.06 Clause #312 (by clausification #[311]): ∀ (a a_1 : Iota), Eq (and a a_1) (not (or (not a) (not a_1)))
% 63.89/64.06 Clause #313 (by forward demodulation #[312, 219]): ∀ (a a_1 : Iota), Eq (and a a_1) (not (implies a (not a_1)))
% 63.89/64.06 Clause #314 (by superposition #[313, 219]): ∀ (a a_1 a_2 : Iota), Eq (implies (implies a (not a_1)) a_2) (or (and a a_1) a_2)
% 63.89/64.06 Clause #329 (by superposition #[314, 313]): ∀ (a a_1 a_2 : Iota), Eq (and (implies a (not a_1)) a_2) (not (or (and a a_1) (not a_2)))
% 63.89/64.06 Clause #331 (by superposition #[314, 271]): ∀ (a a_1 a_2 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (or (and (and (not a_1) a_2) a_1) a)) False)
% 63.89/64.06 Clause #417 (by clausification #[26]): Or (Eq op_or False) (Eq (∀ (X Y : Iota), Eq (or X Y) (not (and (not X) (not Y)))) True)
% 63.89/64.06 Clause #418 (by clausification #[417]): ∀ (a : Iota), Or (Eq op_or False) (Eq (∀ (Y : Iota), Eq (or a Y) (not (and (not a) (not Y)))) True)
% 63.89/64.06 Clause #419 (by clausification #[418]): ∀ (a a_1 : Iota), Or (Eq op_or False) (Eq (Eq (or a a_1) (not (and (not a) (not a_1)))) True)
% 63.89/64.06 Clause #420 (by clausification #[419]): ∀ (a a_1 : Iota), Or (Eq op_or False) (Eq (or a a_1) (not (and (not a) (not a_1))))
% 63.89/64.06 Clause #421 (by forward demodulation #[420, 31]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (or a a_1) (not (and (not a) (not a_1))))
% 63.89/64.06 Clause #422 (by clausification #[421]): ∀ (a a_1 : Iota), Eq (or a a_1) (not (and (not a) (not a_1)))
% 63.89/64.06 Clause #423 (by superposition #[422, 247]): ∀ (a a_1 : Iota), Eq (implies (not a) a_1) (or a a_1)
% 63.89/64.06 Clause #461 (by superposition #[423, 313]): ∀ (a a_1 : Iota), Eq (and (not a) a_1) (not (or a (not a_1)))
% 63.89/64.06 Clause #462 (by superposition #[423, 314]): ∀ (a a_1 a_2 : Iota), Eq (implies (or a (not a_1)) a_2) (or (and (not a) a_1) a_2)
% 63.89/64.06 Clause #470 (by superposition #[423, 247]): ∀ (a a_1 a_2 : Iota), Eq (implies (implies a a_1) a_2) (or (and a (not a_1)) a_2)
% 63.89/64.06 Clause #504 (by superposition #[461, 329]): ∀ (a a_1 a_2 : Iota), Eq (and (implies a (not a_1)) a_2) (and (not (and a a_1)) a_2)
% 63.89/64.06 Clause #545 (by clausification #[30]): Or (Eq op_equiv False) (Eq (∀ (X Y : Iota), Eq (equiv X Y) (and (implies X Y) (implies Y X))) True)
% 63.89/64.06 Clause #546 (by clausification #[545]): ∀ (a : Iota), Or (Eq op_equiv False) (Eq (∀ (Y : Iota), Eq (equiv a Y) (and (implies a Y) (implies Y a))) True)
% 63.89/64.06 Clause #547 (by clausification #[546]): ∀ (a a_1 : Iota), Or (Eq op_equiv False) (Eq (Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a))) True)
% 63.89/64.06 Clause #548 (by clausification #[547]): ∀ (a a_1 : Iota), Or (Eq op_equiv False) (Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a)))
% 63.89/64.06 Clause #549 (by forward demodulation #[548, 33]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a)))
% 63.89/64.06 Clause #550 (by clausification #[549]): ∀ (a a_1 : Iota), Eq (equiv a a_1) (and (implies a a_1) (implies a_1 a))
% 63.89/64.06 Clause #552 (by superposition #[550, 90]): ∀ (a : Iota), Eq (is_a_theorem (implies (implies a a) (equiv a a))) True
% 63.89/64.06 Clause #563 (by superposition #[550, 423]): ∀ (a a_1 : Iota), Eq (equiv a (not a_1)) (and (implies a (not a_1)) (or a_1 a))
% 63.89/64.08 Clause #1264 (by superposition #[504, 247]): ∀ (a a_1 a_2 : Iota), Eq (and (implies a (not (not a_1))) a_2) (and (implies a a_1) a_2)
% 63.89/64.08 Clause #1417 (by superposition #[563, 1264]): ∀ (a a_1 : Iota), Eq (equiv a (not (not a_1))) (and (implies a a_1) (or (not a_1) a))
% 63.89/64.08 Clause #1685 (by forward demodulation #[1417, 219]): ∀ (a a_1 : Iota), Eq (equiv a (not (not a_1))) (and (implies a a_1) (implies a_1 a))
% 63.89/64.08 Clause #1686 (by superposition #[1685, 550]): ∀ (a a_1 : Iota), Eq (equiv a a_1) (equiv a (not (not a_1)))
% 63.89/64.08 Clause #1727 (by superposition #[1686, 97]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (equiv a a_1)) False) (Eq a (not (not a_1)))
% 63.89/64.08 Clause #1850 (by clausification #[263]): ∀ (a : Iota),
% 63.89/64.08 Or (Eq kn3 False)
% 63.89/64.08 (Eq (∀ (Q R : Iota), is_a_theorem (implies (implies a Q) (implies (not (and Q R)) (not (and R a))))) True)
% 63.89/64.08 Clause #1851 (by clausification #[1850]): ∀ (a a_1 : Iota),
% 63.89/64.08 Or (Eq kn3 False)
% 63.89/64.08 (Eq (∀ (R : Iota), is_a_theorem (implies (implies a a_1) (implies (not (and a_1 R)) (not (and R a))))) True)
% 63.89/64.08 Clause #1852 (by clausification #[1851]): ∀ (a a_1 a_2 : Iota),
% 63.89/64.08 Or (Eq kn3 False) (Eq (is_a_theorem (implies (implies a a_1) (implies (not (and a_1 a_2)) (not (and a_2 a))))) True)
% 63.89/64.08 Clause #1853 (by forward demodulation #[1852, 37]): ∀ (a a_1 a_2 : Iota),
% 63.89/64.08 Or (Eq True False) (Eq (is_a_theorem (implies (implies a a_1) (implies (not (and a_1 a_2)) (not (and a_2 a))))) True)
% 63.89/64.08 Clause #1854 (by clausification #[1853]): ∀ (a a_1 a_2 : Iota), Eq (is_a_theorem (implies (implies a a_1) (implies (not (and a_1 a_2)) (not (and a_2 a))))) True
% 63.89/64.08 Clause #1855 (by forward demodulation #[1854, 423]): ∀ (a a_1 a_2 : Iota), Eq (is_a_theorem (implies (implies a a_1) (or (and a_1 a_2) (not (and a_2 a))))) True
% 63.89/64.08 Clause #1857 (by superposition #[1855, 276]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (or (and (and a a) a_1) (not (and a_1 a)))) True) (Eq True False)
% 63.89/64.08 Clause #17419 (by clausification #[1857]): ∀ (a a_1 : Iota), Eq (is_a_theorem (or (and (and a a) a_1) (not (and a_1 a)))) True
% 63.89/64.08 Clause #17420 (by superposition #[17419, 331]): ∀ (a : Iota), Or (Eq (is_a_theorem (not (and a (not a)))) True) (Eq True False)
% 63.89/64.08 Clause #17493 (by clausification #[17420]): ∀ (a : Iota), Eq (is_a_theorem (not (and a (not a)))) True
% 63.89/64.08 Clause #17494 (by forward demodulation #[17493, 247]): ∀ (a : Iota), Eq (is_a_theorem (implies a a)) True
% 63.89/64.08 Clause #17504 (by superposition #[17494, 68]): ∀ (a a_1 : Iota),
% 63.89/64.08 Or (Eq (is_a_theorem a) True) (Or (Eq True False) (Eq (is_a_theorem (implies (implies a_1 a_1) a)) False))
% 63.89/64.08 Clause #20673 (by clausification #[17504]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies a_1 a_1) a)) False)
% 63.89/64.08 Clause #20675 (by superposition #[20673, 552]): ∀ (a : Iota), Or (Eq (is_a_theorem (equiv a a)) True) (Eq False True)
% 63.89/64.08 Clause #20678 (by superposition #[20673, 1855]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (or (and a a_1) (not (and a_1 a)))) True) (Eq False True)
% 63.89/64.08 Clause #20719 (by clausification #[20675]): ∀ (a : Iota), Eq (is_a_theorem (equiv a a)) True
% 63.89/64.08 Clause #20720 (by superposition #[20719, 1727]): ∀ (a : Iota), Or (Eq True False) (Eq a (not (not a)))
% 63.89/64.08 Clause #20737 (by clausification #[20720]): ∀ (a : Iota), Eq a (not (not a))
% 63.89/64.08 Clause #20751 (by superposition #[20737, 247]): ∀ (a a_1 : Iota), Eq (implies a (not a_1)) (not (and a a_1))
% 63.89/64.08 Clause #26949 (by clausification #[20678]): ∀ (a a_1 : Iota), Eq (is_a_theorem (or (and a a_1) (not (and a_1 a)))) True
% 63.89/64.08 Clause #26950 (by forward demodulation #[26949, 20751]): ∀ (a a_1 : Iota), Eq (is_a_theorem (or (and a a_1) (implies a_1 (not a)))) True
% 63.89/64.08 Clause #27014 (by superposition #[26950, 20737]): ∀ (a a_1 : Iota), Eq (is_a_theorem (or (and (not a) a_1) (implies a_1 a))) True
% 63.89/64.08 Clause #27046 (by forward demodulation #[27014, 462]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (or a (not a_1)) (implies a_1 a))) True
% 63.89/64.08 Clause #27125 (by superposition #[27046, 20737]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (or a a_1) (implies (not a_1) a))) True
% 63.89/64.08 Clause #27148 (by forward demodulation #[27125, 423]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True
% 64.03/64.25 Clause #27164 (by superposition #[27148, 219]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (implies a a_1) (or a_1 (not a)))) True
% 64.03/64.25 Clause #27190 (by superposition #[27164, 276]): ∀ (a : Iota), Or (Eq (is_a_theorem (or (and a a) (not a))) True) (Eq True False)
% 64.03/64.25 Clause #27275 (by clausification #[27190]): ∀ (a : Iota), Eq (is_a_theorem (or (and a a) (not a))) True
% 64.03/64.25 Clause #27322 (by superposition #[27275, 20737]): ∀ (a : Iota), Eq (is_a_theorem (or (and (not a) (not a)) a)) True
% 64.03/64.25 Clause #27346 (by forward demodulation #[27322, 470]): ∀ (a : Iota), Eq (is_a_theorem (implies (implies (not a) a) a)) True
% 64.03/64.25 Clause #27347 (by forward demodulation #[27346, 423]): ∀ (a : Iota), Eq (is_a_theorem (implies (or a a) a)) True
% 64.03/64.25 Clause #27348 (by superposition #[27347, 74]): Eq True False
% 64.03/64.25 Clause #27374 (by clausification #[27348]): False
% 64.03/64.25 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------