0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.33	% Computer   : n027.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 180
0.13/0.33	% DateTime   : Thu Aug 29 10:05:54 EDT 2019
0.13/0.33	% CPUTime    : 
0.19/0.47	% SZS status Theorem
0.19/0.47	
0.19/0.47	% SZS output start Proof
0.19/0.47	Take the following subset of the input axioms:
0.19/0.51	  fof(p1, axiom, ![B]: (ilf_type(B, binary_relation_type) => image(B, domain_of(B))=range_of(B))).
0.19/0.51	  fof(p12, axiom, ![B]: (ilf_type(B, set_type) => ((relation_like(B) & ilf_type(B, set_type)) <=> ilf_type(B, binary_relation_type)))).
0.19/0.51	  fof(p2, axiom, ![B]: (inverse2(B, range_of(B))=domain_of(B) <= ilf_type(B, binary_relation_type))).
0.19/0.51	  fof(p23, axiom, ![B]: (ilf_type(B, set_type) => ![C]: (ilf_type(C, set_type) => ![D]: (ilf_type(D, subset_type(cross_product(B, C))) => relation_like(D))))).
0.19/0.51	  fof(p27, axiom, ![B]: (![C]: (ilf_type(C, set_type) => ![D]: (domain(B, C, D)=domain_of(D) <= ilf_type(D, relation_type(B, C)))) <= ilf_type(B, set_type))).
0.19/0.51	  fof(p29, axiom, ![B]: (![C]: (![D]: (range_of(D)=range(B, C, D) <= ilf_type(D, relation_type(B, C))) <= ilf_type(C, set_type)) <= ilf_type(B, set_type))).
0.19/0.51	  fof(p3, axiom, ![B]: (![C]: (ilf_type(C, set_type) => ![D]: ((inverse4(B, C, D, C)=domain(B, C, D) & range(B, C, D)=image4(B, C, D, B)) <= ilf_type(D, relation_type(B, C)))) <= ilf_type(B, set_type))).
0.19/0.51	  fof(p31, axiom, ![B]: (ilf_type(B, set_type) => ![C]: (![D]: (![E]: (image(D, E)=image4(B, C, D, E) <= ilf_type(E, set_type)) <= ilf_type(D, relation_type(B, C))) <= ilf_type(C, set_type)))).
0.19/0.51	  fof(p33, axiom, ![B]: (ilf_type(B, set_type) => ![C]: (![D]: (ilf_type(D, relation_type(B, C)) => ![E]: (inverse4(B, C, D, E)=inverse2(D, E) <= ilf_type(E, set_type))) <= ilf_type(C, set_type)))).
0.19/0.51	  fof(p35, axiom, ![B]: ilf_type(B, set_type)).
0.19/0.51	  fof(p4, axiom, ![B]: (ilf_type(B, set_type) => ![C]: (ilf_type(C, set_type) => (![E]: (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))) & ![D]: (ilf_type(D, relation_type(B, C)) <= ilf_type(D, subset_type(cross_product(B, C)))))))).
0.19/0.51	  fof(prove_relset_1_39, conjecture, ![B]: (![C]: (![D]: ((domain(C, B, D)=inverse4(C, B, D, image4(C, B, D, C)) & range(C, B, D)=image4(C, B, D, inverse4(C, B, D, B))) <= ilf_type(D, relation_type(C, B))) <= ilf_type(C, set_type)) <= ilf_type(B, set_type))).
0.19/0.51	
0.19/0.51	Now clausify the problem and encode Horn clauses using encoding 3 of
0.19/0.51	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.19/0.51	We repeatedly replace C & s=t => u=v by the two clauses:
0.19/0.51	  fresh(y, y, x1...xn) = u
0.19/0.51	  C => fresh(s, t, x1...xn) = v
0.19/0.51	where fresh is a fresh function symbol and x1..xn are the free
0.19/0.51	variables of u and v.
0.19/0.51	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.19/0.51	input problem has no model of domain size 1).
0.19/0.51	
0.19/0.51	The encoding turns the above axioms into the following unit equations and goals:
0.19/0.51	
0.19/0.51	Axiom 1 (p1): fresh36(X, X, Y) = range_of(Y).
0.19/0.51	Axiom 2 (p12_1): fresh31(X, X, Y) = ilf_type(Y, binary_relation_type).
0.19/0.51	Axiom 3 (p12_1): fresh30(X, X, Y) = true2.
0.19/0.51	Axiom 4 (p2): fresh22(X, X, Y) = domain_of(Y).
0.19/0.51	Axiom 5 (p23): fresh21(X, X, Y, Z) = relation_like(Z).
0.19/0.51	Axiom 6 (p23): fresh84(X, X, Y) = true2.
0.19/0.51	Axiom 7 (p23): fresh83(X, X, Y, Z, W) = fresh84(ilf_type(Y, set_type), true2, W).
0.19/0.51	Axiom 8 (p27): fresh16(X, X, Y, Z, W) = domain(Y, Z, W).
0.19/0.51	Axiom 9 (p27): fresh54(X, X, Y, Z, W) = domain_of(W).
0.19/0.51	Axiom 10 (p27): fresh53(X, X, Y, Z, W) = fresh54(ilf_type(Y, set_type), true2, Y, Z, W).
0.19/0.51	Axiom 11 (p29): fresh14(X, X, Y, Z, W) = range(Y, Z, W).
0.19/0.51	Axiom 12 (p29): fresh56(X, X, Y, Z, W) = range_of(W).
0.19/0.51	Axiom 13 (p29): fresh55(X, X, Y, Z, W) = fresh56(ilf_type(Y, set_type), true2, Y, Z, W).
0.19/0.51	Axiom 14 (p3): fresh107(X, X, Y, Z, W) = domain(Y, Z, W).
0.19/0.51	Axiom 15 (p3): fresh13(X, X, Y, Z, W) = inverse4(Y, Z, W, Z).
0.19/0.51	Axiom 16 (p3): fresh106(X, X, Y, Z, W) = fresh107(ilf_type(Y, set_type), true2, Y, Z, W).
0.19/0.51	Axiom 17 (p31): fresh43(X, X, Y, Z, W, V) = image4(Y, Z, W, V).
0.19/0.51	Axiom 18 (p31): fresh45(X, X, Y, Z, W, V) = image(W, V).
0.19/0.51	Axiom 19 (p31): fresh44(X, X, Y, Z, W, V) = fresh45(ilf_type(Y, set_type), true2, Y, Z, W, V).
0.19/0.51	Axiom 20 (p31): fresh42(X, X, Y, Z, W, V) = fresh43(ilf_type(Z, set_type), true2, Y, Z, W, V).
0.19/0.51	Axiom 21 (p33): fresh86(X, X, Y, Z, W, V) = inverse4(Y, Z, W, V).
0.19/0.51	Axiom 22 (p33): fresh88(X, X, Y, Z, W, V) = inverse2(W, V).
0.19/0.51	Axiom 23 (p33): fresh87(X, X, Y, Z, W, V) = fresh88(ilf_type(Y, set_type), true2, Y, Z, W, V).
0.19/0.51	Axiom 24 (p33): fresh85(X, X, Y, Z, W, V) = fresh86(ilf_type(Z, set_type), true2, Y, Z, W, V).
0.19/0.51	Axiom 25 (p3_1): fresh11(X, X, Y, Z, W) = image4(Y, Z, W, Y).
0.19/0.51	Axiom 26 (p3_1): fresh109(X, X, Y, Z, W) = range(Y, Z, W).
0.19/0.51	Axiom 27 (p3_1): fresh108(X, X, Y, Z, W) = fresh109(ilf_type(Y, set_type), true2, Y, Z, W).
0.19/0.51	Axiom 28 (p4): fresh10(X, X, Y, Z, W) = ilf_type(W, subset_type(cross_product(Y, Z))).
0.19/0.51	Axiom 29 (p4): fresh97(X, X, Y, Z, W) = true2.
0.19/0.51	Axiom 30 (p4): fresh96(X, X, Y, Z, W) = fresh97(ilf_type(Y, set_type), true2, Y, Z, W).
0.19/0.51	Axiom 31 (p3_1): fresh108(ilf_type(X, relation_type(Y, Z)), true2, Y, Z, X) = fresh11(ilf_type(Z, set_type), true2, Y, Z, X).
0.19/0.51	Axiom 32 (p3): fresh106(ilf_type(X, relation_type(Y, Z)), true2, Y, Z, X) = fresh13(ilf_type(Z, set_type), true2, Y, Z, X).
0.19/0.51	Axiom 33 (p35): ilf_type(X, set_type) = true2.
0.19/0.51	Axiom 34 (p4): fresh96(ilf_type(X, relation_type(Y, Z)), true2, Y, Z, X) = fresh10(ilf_type(Z, set_type), true2, Y, Z, X).
0.19/0.51	Axiom 35 (p12_1): fresh31(relation_like(X), true2, X) = fresh30(ilf_type(X, set_type), true2, X).
0.19/0.51	Axiom 36 (p33): fresh85(ilf_type(X, set_type), true2, Y, Z, W, X) = fresh87(ilf_type(W, relation_type(Y, Z)), true2, Y, Z, W, X).
0.19/0.51	Axiom 37 (p23): fresh83(ilf_type(X, subset_type(cross_product(Y, Z))), true2, Y, Z, X) = fresh21(ilf_type(Z, set_type), true2, Y, X).
0.19/0.51	Axiom 38 (p2): fresh22(ilf_type(X, binary_relation_type), true2, X) = inverse2(X, range_of(X)).
0.19/0.51	Axiom 39 (p29): fresh55(ilf_type(X, relation_type(Y, Z)), true2, Y, Z, X) = fresh14(ilf_type(Z, set_type), true2, Y, Z, X).
0.19/0.51	Axiom 40 (p27): fresh53(ilf_type(X, relation_type(Y, Z)), true2, Y, Z, X) = fresh16(ilf_type(Z, set_type), true2, Y, Z, X).
0.19/0.51	Axiom 41 (p1): fresh36(ilf_type(X, binary_relation_type), true2, X) = image(X, domain_of(X)).
0.19/0.51	Axiom 42 (p31): fresh42(ilf_type(X, set_type), true2, Y, Z, W, X) = fresh44(ilf_type(W, relation_type(Y, Z)), true2, Y, Z, W, X).
0.19/0.51	Axiom 43 (prove_relset_1_39_2): ilf_type(sK4_prove_relset_1_39_D, relation_type(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B)) = true2.
0.19/0.51	
0.19/0.51	Lemma 44: domain(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D) = domain_of(sK4_prove_relset_1_39_D).
0.19/0.51	Proof:
0.19/0.51	  domain(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 8 (p27) }
0.19/0.51	  fresh16(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh16(ilf_type(sK6_prove_relset_1_39_B, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 40 (p27) }
0.19/0.51	  fresh53(ilf_type(sK4_prove_relset_1_39_D, relation_type(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B)), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 43 (prove_relset_1_39_2) }
0.19/0.51	  fresh53(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 10 (p27) }
0.19/0.51	  fresh54(ilf_type(sK5_prove_relset_1_39_C, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh54(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 9 (p27) }
0.19/0.51	  domain_of(sK4_prove_relset_1_39_D)
0.19/0.51	
0.19/0.51	Lemma 45: ilf_type(sK4_prove_relset_1_39_D, binary_relation_type) = true2.
0.19/0.51	Proof:
0.19/0.51	  ilf_type(sK4_prove_relset_1_39_D, binary_relation_type)
0.19/0.51	= { by axiom 2 (p12_1) }
0.19/0.51	  fresh31(true2, true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 6 (p23) }
0.19/0.51	  fresh31(fresh84(true2, true2, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh31(fresh84(ilf_type(sK5_prove_relset_1_39_C, set_type), true2, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 7 (p23) }
0.19/0.51	  fresh31(fresh83(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 29 (p4) }
0.19/0.51	  fresh31(fresh83(fresh97(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh31(fresh83(fresh97(ilf_type(sK5_prove_relset_1_39_C, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 30 (p4) }
0.19/0.51	  fresh31(fresh83(fresh96(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 43 (prove_relset_1_39_2) }
0.19/0.51	  fresh31(fresh83(fresh96(ilf_type(sK4_prove_relset_1_39_D, relation_type(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B)), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 34 (p4) }
0.19/0.51	  fresh31(fresh83(fresh10(ilf_type(sK6_prove_relset_1_39_B, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh31(fresh83(fresh10(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 28 (p4) }
0.19/0.51	  fresh31(fresh83(ilf_type(sK4_prove_relset_1_39_D, subset_type(cross_product(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B))), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 37 (p23) }
0.19/0.51	  fresh31(fresh21(ilf_type(sK6_prove_relset_1_39_B, set_type), true2, sK5_prove_relset_1_39_C, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh31(fresh21(true2, true2, sK5_prove_relset_1_39_C, sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 5 (p23) }
0.19/0.51	  fresh31(relation_like(sK4_prove_relset_1_39_D), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 35 (p12_1) }
0.19/0.51	  fresh30(ilf_type(sK4_prove_relset_1_39_D, set_type), true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh30(true2, true2, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 3 (p12_1) }
0.19/0.51	  true2
0.19/0.51	
0.19/0.51	Lemma 46: range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D) = range_of(sK4_prove_relset_1_39_D).
0.19/0.51	Proof:
0.19/0.51	  range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 11 (p29) }
0.19/0.51	  fresh14(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh14(ilf_type(sK6_prove_relset_1_39_B, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 39 (p29) }
0.19/0.51	  fresh55(ilf_type(sK4_prove_relset_1_39_D, relation_type(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B)), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 43 (prove_relset_1_39_2) }
0.19/0.51	  fresh55(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 13 (p29) }
0.19/0.51	  fresh56(ilf_type(sK5_prove_relset_1_39_C, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 33 (p35) }
0.19/0.51	  fresh56(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)
0.19/0.51	= { by axiom 12 (p29) }
0.19/0.55	  range_of(sK4_prove_relset_1_39_D)
0.19/0.55	
0.19/0.55	Goal 1 (prove_relset_1_39_3): tuple3(domain(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)) = tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK6_prove_relset_1_39_B))).
0.19/0.55	Proof:
0.19/0.55	  tuple3(domain(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by lemma 44 }
0.19/0.55	  tuple3(domain_of(sK4_prove_relset_1_39_D), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 4 (p2) }
0.19/0.55	  tuple3(fresh22(true2, true2, sK4_prove_relset_1_39_D), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by lemma 45 }
0.19/0.55	  tuple3(fresh22(ilf_type(sK4_prove_relset_1_39_D, binary_relation_type), true2, sK4_prove_relset_1_39_D), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 38 (p2) }
0.19/0.55	  tuple3(inverse2(sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 22 (p33) }
0.19/0.55	  tuple3(fresh88(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(fresh88(ilf_type(sK5_prove_relset_1_39_C, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 23 (p33) }
0.19/0.55	  tuple3(fresh87(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 43 (prove_relset_1_39_2) }
0.19/0.55	  tuple3(fresh87(ilf_type(sK4_prove_relset_1_39_D, relation_type(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B)), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 36 (p33) }
0.19/0.55	  tuple3(fresh85(ilf_type(range_of(sK4_prove_relset_1_39_D), set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(fresh85(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 24 (p33) }
0.19/0.55	  tuple3(fresh86(ilf_type(sK6_prove_relset_1_39_B, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(fresh86(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 21 (p33) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range_of(sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by lemma 46 }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 26 (p3_1) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh109(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh109(ilf_type(sK5_prove_relset_1_39_C, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 27 (p3_1) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh108(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 43 (prove_relset_1_39_2) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh108(ilf_type(sK4_prove_relset_1_39_D, relation_type(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B)), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 31 (p3_1) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh11(ilf_type(sK6_prove_relset_1_39_B, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh11(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 25 (p3_1) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), range(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D))
0.19/0.55	= { by lemma 46 }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), range_of(sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 1 (p1) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh36(true2, true2, sK4_prove_relset_1_39_D))
0.19/0.55	= { by lemma 45 }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh36(ilf_type(sK4_prove_relset_1_39_D, binary_relation_type), true2, sK4_prove_relset_1_39_D))
0.19/0.55	= { by axiom 41 (p1) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image(sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 18 (p31) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh45(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh45(ilf_type(sK5_prove_relset_1_39_C, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 19 (p31) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh44(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 43 (prove_relset_1_39_2) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh44(ilf_type(sK4_prove_relset_1_39_D, relation_type(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B)), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 42 (p31) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh42(ilf_type(domain_of(sK4_prove_relset_1_39_D), set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh42(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 20 (p31) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh43(ilf_type(sK6_prove_relset_1_39_B, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), fresh43(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 17 (p31) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain_of(sK4_prove_relset_1_39_D)))
0.19/0.55	= { by lemma 44 }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, domain(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 14 (p3) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh107(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh107(ilf_type(sK5_prove_relset_1_39_C, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 16 (p3) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh106(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 43 (prove_relset_1_39_2) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh106(ilf_type(sK4_prove_relset_1_39_D, relation_type(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B)), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 32 (p3) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh13(ilf_type(sK6_prove_relset_1_39_B, set_type), true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 33 (p35) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, fresh13(true2, true2, sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D)))
0.19/0.55	= { by axiom 15 (p3) }
0.19/0.55	  tuple3(inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK5_prove_relset_1_39_C)), image4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, inverse4(sK5_prove_relset_1_39_C, sK6_prove_relset_1_39_B, sK4_prove_relset_1_39_D, sK6_prove_relset_1_39_B)))
0.19/0.55	% SZS output end Proof
0.19/0.55	
0.19/0.55	RESULT: Theorem (the conjecture is true).
0.19/0.55	EOF