0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : duper %s
0.12/0.33	% Computer : n028.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1440
0.12/0.33	% WCLimit    : 180
0.12/0.33	% DateTime   : Mon Jul  3 05:05:28 EDT 2023
0.12/0.33	% CPUTime    : 
71.37/71.57	SZS status Theorem for theBenchmark.p
71.37/71.57	SZS output start Proof for theBenchmark.p
71.37/71.57	Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx))
71.37/71.57	  True
71.37/71.57	Clause #3 (by assumption #[]): Eq (Eq kpairp (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy))) True
71.37/71.57	Clause #5 (by assumption #[]): Eq (Eq theprop (∀ (X : Iota), singleton X → in (setunion X) X)) True
71.37/71.57	Clause #6 (by assumption #[]): Eq (Eq setukpairinjR (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu)) True
71.37/71.57	Clause #7 (by assumption #[]): Eq
71.37/71.57	  (Eq ksndsingleton
71.37/71.57	    (∀ (Xu : Iota), iskpair Xu → singleton (dsetconstr (setunion Xu) fun Xx => Eq Xu (kpair (kfst Xu) Xx))))
71.37/71.57	  True
71.37/71.57	Clause #8 (by assumption #[]): Eq (Eq ksnd fun Xu => setunion (dsetconstr (setunion Xu) fun Xx => Eq Xu (kpair (kfst Xu) Xx))) True
71.37/71.57	Clause #9 (by assumption #[]): Eq
71.37/71.57	  (Not (dsetconstrER → kpairp → theprop → setukpairinjR → ksndsingleton → ∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy))
71.37/71.57	  True
71.37/71.57	Clause #10 (by clausification #[5]): Eq theprop (∀ (X : Iota), singleton X → in (setunion X) X)
71.37/71.57	Clause #20 (by clausification #[3]): Eq kpairp (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy))
71.37/71.57	Clause #22 (by clausify Prop equality #[20]): Or (Eq kpairp False) (Eq (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) True)
71.37/71.57	Clause #24 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True
71.37/71.57	Clause #25 (by clausification #[24]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)
71.37/71.57	Clause #41 (by clausification #[22]): ∀ (a : Iota), Or (Eq kpairp False) (Eq (∀ (Xy : Iota), iskpair (kpair a Xy)) True)
71.37/71.57	Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq kpairp False) (Eq (iskpair (kpair a a_1)) True)
71.37/71.57	Clause #49 (by clausification #[6]): Eq setukpairinjR (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu)
71.37/71.57	Clause #51 (by clausify Prop equality #[49]): Or (Eq setukpairinjR False) (Eq (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu) True)
71.37/71.57	Clause #53 (by clausification #[51]): ∀ (a : Iota), Or (Eq setukpairinjR False) (Eq (∀ (Xy Xz Xu : Iota), Eq (kpair a Xy) (kpair Xz Xu) → Eq Xy Xu) True)
71.37/71.57	Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Or (Eq setukpairinjR False) (Eq (∀ (Xz Xu : Iota), Eq (kpair a a_1) (kpair Xz Xu) → Eq a_1 Xu) True)
71.37/71.57	Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq setukpairinjR False) (Eq (∀ (Xu : Iota), Eq (kpair a a_1) (kpair a_2 Xu) → Eq a_1 Xu) True)
71.37/71.57	Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq setukpairinjR False) (Eq (Eq (kpair a a_1) (kpair a_2 a_3) → Eq a_1 a_3) True)
71.37/71.57	Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota),
71.37/71.57	  Or (Eq setukpairinjR False) (Or (Eq (Eq (kpair a a_1) (kpair a_2 a_3)) False) (Eq (Eq a_1 a_3) True))
71.37/71.57	Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq setukpairinjR False) (Or (Eq (Eq a a_1) True) (Ne (kpair a_2 a) (kpair a_3 a_1)))
71.37/71.57	Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq setukpairinjR False) (Or (Ne (kpair a a_1) (kpair a_2 a_3)) (Eq a_1 a_3))
71.37/71.57	Clause #74 (by clausification #[9]): Eq (dsetconstrER → kpairp → theprop → setukpairinjR → ksndsingleton → ∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy)
71.37/71.57	  False
71.37/71.57	Clause #75 (by clausification #[74]): Eq dsetconstrER True
71.37/71.57	Clause #76 (by clausification #[74]): Eq (kpairp → theprop → setukpairinjR → ksndsingleton → ∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) False
71.37/71.57	Clause #77 (by backward demodulation #[75, 25]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)
71.37/71.57	Clause #80 (by clausification #[77]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True
71.37/71.57	Clause #81 (by clausification #[80]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True
71.37/71.59	Clause #82 (by clausification #[81]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True
71.37/71.59	Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True)
71.37/71.59	Clause #103 (by clausification #[76]): Eq kpairp True
71.37/71.59	Clause #104 (by clausification #[76]): Eq (theprop → setukpairinjR → ksndsingleton → ∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) False
71.37/71.59	Clause #106 (by backward demodulation #[103, 42]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (iskpair (kpair a a_1)) True)
71.37/71.59	Clause #110 (by clausification #[106]): ∀ (a a_1 : Iota), Eq (iskpair (kpair a a_1)) True
71.37/71.59	Clause #115 (by clausification #[7]): Eq ksndsingleton (∀ (Xu : Iota), iskpair Xu → singleton (dsetconstr (setunion Xu) fun Xx => Eq Xu (kpair (kfst Xu) Xx)))
71.37/71.59	Clause #122 (by clausification #[104]): Eq theprop True
71.37/71.59	Clause #123 (by clausification #[104]): Eq (setukpairinjR → ksndsingleton → ∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) False
71.37/71.59	Clause #124 (by backward demodulation #[122, 10]): Eq True (∀ (X : Iota), singleton X → in (setunion X) X)
71.37/71.59	Clause #130 (by clausification #[124]): ∀ (a : Iota), Eq (singleton a → in (setunion a) a) True
71.37/71.59	Clause #131 (by clausification #[130]): ∀ (a : Iota), Or (Eq (singleton a) False) (Eq (in (setunion a) a) True)
71.37/71.59	Clause #134 (by clausification #[8]): Eq ksnd fun Xu => setunion (dsetconstr (setunion Xu) fun Xx => Eq Xu (kpair (kfst Xu) Xx))
71.37/71.59	Clause #135 (by argument congruence #[134]): ∀ (a : Iota), Eq (ksnd a) ((fun Xu => setunion (dsetconstr (setunion Xu) fun Xx => Eq Xu (kpair (kfst Xu) Xx))) a)
71.37/71.59	Clause #140 (by clausification #[123]): Eq setukpairinjR True
71.37/71.59	Clause #141 (by clausification #[123]): Eq (ksndsingleton → ∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) False
71.37/71.59	Clause #143 (by backward demodulation #[140, 59]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Or (Ne (kpair a a_1) (kpair a_2 a_3)) (Eq a_1 a_3))
71.37/71.59	Clause #149 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (kpair a a_1) (kpair a_2 a_3)) (Eq a_1 a_3)
71.37/71.59	Clause #160 (by clausification #[141]): Eq ksndsingleton True
71.37/71.59	Clause #161 (by clausification #[141]): Eq (∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) False
71.37/71.59	Clause #162 (by backward demodulation #[160, 115]): Eq True (∀ (Xu : Iota), iskpair Xu → singleton (dsetconstr (setunion Xu) fun Xx => Eq Xu (kpair (kfst Xu) Xx)))
71.37/71.59	Clause #165 (by clausification #[161]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), Eq (ksnd (kpair (skS.0 10 a) Xy)) Xy)) True
71.37/71.59	Clause #166 (by clausification #[165]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Eq (ksnd (kpair (skS.0 10 a) Xy)) Xy) False
71.37/71.59	Clause #167 (by clausification #[166]): ∀ (a a_1 : Iota), Eq (Not (Eq (ksnd (kpair (skS.0 10 a) (skS.0 11 a a_1))) (skS.0 11 a a_1))) True
71.37/71.59	Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (Eq (ksnd (kpair (skS.0 10 a) (skS.0 11 a a_1))) (skS.0 11 a a_1)) False
71.37/71.59	Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), Ne (ksnd (kpair (skS.0 10 a) (skS.0 11 a a_1))) (skS.0 11 a a_1)
71.37/71.59	Clause #180 (by clausification #[162]): ∀ (a : Iota), Eq (iskpair a → singleton (dsetconstr (setunion a) fun Xx => Eq a (kpair (kfst a) Xx))) True
71.37/71.59	Clause #181 (by clausification #[180]): ∀ (a : Iota),
71.37/71.59	  Or (Eq (iskpair a) False) (Eq (singleton (dsetconstr (setunion a) fun Xx => Eq a (kpair (kfst a) Xx))) True)
71.37/71.59	Clause #182 (by superposition #[181, 110]): ∀ (a a_1 : Iota),
71.37/71.59	  Or
71.37/71.59	    (Eq (singleton (dsetconstr (setunion (kpair a a_1)) fun Xx => Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) Xx)))
71.37/71.59	      True)
71.37/71.59	    (Eq False True)
71.37/71.59	Clause #193 (by betaEtaReduce #[135]): ∀ (a : Iota), Eq (ksnd a) (setunion (dsetconstr (setunion a) fun Xx => Eq a (kpair (kfst a) Xx)))
71.37/71.59	Clause #566 (by clausification #[182]): ∀ (a a_1 : Iota),
71.37/71.59	  Eq (singleton (dsetconstr (setunion (kpair a a_1)) fun Xx => Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) Xx))) True
71.37/71.59	Clause #567 (by superposition #[566, 131]): ∀ (a a_1 : Iota),
71.37/71.59	  Or (Eq True False)
71.37/71.59	    (Eq
71.37/71.59	      (in (setunion (dsetconstr (setunion (kpair a a_1)) fun Xx => Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) Xx)))
72.23/72.41	        (dsetconstr (setunion (kpair a a_1)) fun Xx => Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) Xx)))
72.23/72.41	      True)
72.23/72.41	Clause #8289 (by clausification #[567]): ∀ (a a_1 : Iota),
72.23/72.41	  Eq
72.23/72.41	    (in (setunion (dsetconstr (setunion (kpair a a_1)) fun Xx => Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) Xx)))
72.23/72.41	      (dsetconstr (setunion (kpair a a_1)) fun Xx => Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) Xx)))
72.23/72.41	    True
72.23/72.41	Clause #8290 (by forward demodulation #[8289, 193]): ∀ (a a_1 : Iota),
72.23/72.41	  Eq
72.23/72.41	    (in (ksnd (kpair a a_1))
72.23/72.41	      (dsetconstr (setunion (kpair a a_1)) fun Xx => Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) Xx)))
72.23/72.41	    True
72.23/72.41	Clause #8291 (by superposition #[8290, 83]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) (ksnd (kpair a a_1)))) True)
72.23/72.41	Clause #8709 (by clausification #[8291]): ∀ (a a_1 : Iota), Eq (Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) (ksnd (kpair a a_1)))) True
72.23/72.41	Clause #8710 (by clausification #[8709]): ∀ (a a_1 : Iota), Eq (kpair a a_1) (kpair (kfst (kpair a a_1)) (ksnd (kpair a a_1)))
72.23/72.41	Clause #8712 (by superposition #[8710, 149]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (kpair a a_1) (kpair a_2 a_3)) (Eq a_1 (ksnd (kpair a_2 a_3)))
72.23/72.41	Clause #8779 (by equality resolution #[8712]): ∀ (a a_1 : Iota), Eq a (ksnd (kpair a_1 a))
72.23/72.41	Clause #8784 (by backward contextual literal cutting #[8779, 169]): False
72.23/72.41	SZS output end Proof for theBenchmark.p
72.23/72.43	EOF