TSTP Solution File: SEU039+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n020.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 17:50:51 EDT 2023
% Result : Theorem 0.19s 0.73s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n020.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 : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 01:32:00 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.73 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.73
% 0.19/0.73 % SZS status Theorem
% 0.19/0.73
% 0.19/0.75 % SZS output start Proof
% 0.19/0.76 Take the following subset of the input axioms:
% 0.19/0.76 fof(commutativity_k3_xboole_0, axiom, ![A, B]: set_intersection2(A, B)=set_intersection2(B, A)).
% 0.19/0.76 fof(d3_xboole_0, axiom, ![C, A2, B2]: (C=set_intersection2(A2, B2) <=> ![D]: (in(D, C) <=> (in(D, A2) & in(D, B2))))).
% 0.19/0.76 fof(d5_funct_1, axiom, ![A2_2]: ((relation(A2_2) & function(A2_2)) => ![B2]: (B2=relation_rng(A2_2) <=> ![C2]: (in(C2, B2) <=> ?[D2]: (in(D2, relation_dom(A2_2)) & C2=apply(A2_2, D2)))))).
% 0.19/0.76 fof(dt_k7_relat_1, axiom, ![B2, A2_2]: (relation(A2_2) => relation(relation_dom_restriction(A2_2, B2)))).
% 0.19/0.76 fof(fc4_funct_1, axiom, ![B2, A2_2]: ((relation(A2_2) & function(A2_2)) => (relation(relation_dom_restriction(A2_2, B2)) & function(relation_dom_restriction(A2_2, B2))))).
% 0.19/0.76 fof(t68_funct_1, axiom, ![B2, A2_2]: ((relation(B2) & function(B2)) => ![C2]: ((relation(C2) & function(C2)) => (B2=relation_dom_restriction(C2, A2_2) <=> (relation_dom(B2)=set_intersection2(relation_dom(C2), A2_2) & ![D2]: (in(D2, relation_dom(B2)) => apply(B2, D2)=apply(C2, D2))))))).
% 0.19/0.76 fof(t72_funct_1, axiom, ![B2, C2, A2_2]: ((relation(C2) & function(C2)) => (in(B2, A2_2) => apply(relation_dom_restriction(C2, A2_2), B2)=apply(C2, B2)))).
% 0.19/0.76 fof(t73_funct_1, conjecture, ![A3, B2, C2]: ((relation(C2) & function(C2)) => ((in(B2, relation_dom(C2)) & in(B2, A3)) => in(apply(C2, B2), relation_rng(relation_dom_restriction(C2, A3)))))).
% 0.19/0.76
% 0.19/0.76 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.76 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.76 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.76 fresh(y, y, x1...xn) = u
% 0.19/0.76 C => fresh(s, t, x1...xn) = v
% 0.19/0.76 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.76 variables of u and v.
% 0.19/0.76 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.76 input problem has no model of domain size 1).
% 0.19/0.76
% 0.19/0.76 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.76
% 0.19/0.76 Axiom 1 (t73_funct_1_3): relation(c) = true2.
% 0.19/0.76 Axiom 2 (t73_funct_1_2): function(c) = true2.
% 0.19/0.76 Axiom 3 (t73_funct_1_1): in(b, a) = true2.
% 0.19/0.76 Axiom 4 (commutativity_k3_xboole_0): set_intersection2(X, Y) = set_intersection2(Y, X).
% 0.19/0.76 Axiom 5 (t73_funct_1): in(b, relation_dom(c)) = true2.
% 0.19/0.76 Axiom 6 (d5_funct_1_1): fresh74(X, X, Y, Z) = true2.
% 0.19/0.76 Axiom 7 (d3_xboole_0_2): fresh45(X, X, Y, Z) = true2.
% 0.19/0.76 Axiom 8 (d5_funct_1_2): fresh37(X, X, Y, Z) = true2.
% 0.19/0.76 Axiom 9 (dt_k7_relat_1): fresh35(X, X, Y, Z) = true2.
% 0.19/0.76 Axiom 10 (fc4_funct_1): fresh28(X, X, Y, Z) = function(relation_dom_restriction(Y, Z)).
% 0.19/0.76 Axiom 11 (fc4_funct_1): fresh27(X, X, Y, Z) = true2.
% 0.19/0.76 Axiom 12 (d5_funct_1_1): fresh73(X, X, Y, Z, W) = fresh74(Z, relation_rng(Y), Z, W).
% 0.19/0.76 Axiom 13 (d5_funct_1_1): fresh72(X, X, Y, Z, W) = in(W, Z).
% 0.19/0.76 Axiom 14 (t68_funct_1_1): fresh62(X, X, Y, Z, W) = set_intersection2(relation_dom(W), Y).
% 0.19/0.76 Axiom 15 (t72_funct_1): fresh53(X, X, Y, Z, W) = apply(relation_dom_restriction(Z, Y), W).
% 0.19/0.76 Axiom 16 (d3_xboole_0_3): fresh44(X, X, Y, Z, W) = equiv2(Y, Z, W).
% 0.19/0.76 Axiom 17 (d3_xboole_0_3): fresh43(X, X, Y, Z, W) = true2.
% 0.19/0.76 Axiom 18 (d5_funct_1_2): fresh38(X, X, Y, Z, W) = equiv(Y, Z).
% 0.19/0.76 Axiom 19 (dt_k7_relat_1): fresh35(relation(X), true2, X, Y) = relation(relation_dom_restriction(X, Y)).
% 0.19/0.76 Axiom 20 (fc4_funct_1): fresh28(relation(X), true2, X, Y) = fresh27(function(X), true2, X, Y).
% 0.19/0.76 Axiom 21 (t68_funct_1_1): fresh9(X, X, Y, Z, W) = relation_dom(Z).
% 0.19/0.77 Axiom 22 (t72_funct_1): fresh6(X, X, Y, Z, W) = apply(Z, W).
% 0.19/0.77 Axiom 23 (d5_funct_1_1): fresh71(X, X, Y, Z, W) = fresh72(function(Y), true2, Y, Z, W).
% 0.19/0.77 Axiom 24 (t68_funct_1_1): fresh61(X, X, Y, Z, W) = fresh62(function(Z), true2, Y, Z, W).
% 0.19/0.77 Axiom 25 (t68_funct_1_1): fresh60(X, X, Y, Z, W) = fresh61(function(W), true2, Y, Z, W).
% 0.19/0.77 Axiom 26 (t68_funct_1_1): fresh59(X, X, Y, Z, W) = fresh60(relation(Z), true2, Y, Z, W).
% 0.19/0.77 Axiom 27 (t72_funct_1): fresh52(X, X, Y, Z, W) = fresh53(function(Z), true2, Y, Z, W).
% 0.19/0.77 Axiom 28 (d3_xboole_0_2): fresh46(X, X, Y, Z, W, V) = in(V, W).
% 0.19/0.77 Axiom 29 (d5_funct_1_1): fresh71(equiv(X, Y), true2, X, Z, Y) = fresh73(relation(X), true2, X, Z, Y).
% 0.19/0.77 Axiom 30 (d3_xboole_0_3): fresh44(in(X, Y), true2, Z, Y, X) = fresh43(in(X, Z), true2, Z, Y, X).
% 0.19/0.77 Axiom 31 (t68_funct_1_1): fresh59(relation(X), true2, Y, Z, X) = fresh9(Z, relation_dom_restriction(X, Y), Y, Z, X).
% 0.19/0.77 Axiom 32 (t72_funct_1): fresh52(relation(X), true2, Y, X, Z) = fresh6(in(Z, Y), true2, Y, X, Z).
% 0.19/0.77 Axiom 33 (d5_funct_1_2): fresh38(in(X, relation_dom(Y)), true2, Y, Z, X) = fresh37(Z, apply(Y, X), Y, Z).
% 0.19/0.77 Axiom 34 (d3_xboole_0_2): fresh46(equiv2(X, Y, Z), true2, X, Y, W, Z) = fresh45(W, set_intersection2(X, Y), W, Z).
% 0.19/0.77
% 0.19/0.77 Lemma 35: function(relation_dom_restriction(c, X)) = true2.
% 0.19/0.77 Proof:
% 0.19/0.77 function(relation_dom_restriction(c, X))
% 0.19/0.77 = { by axiom 10 (fc4_funct_1) R->L }
% 0.19/0.77 fresh28(true2, true2, c, X)
% 0.19/0.77 = { by axiom 1 (t73_funct_1_3) R->L }
% 0.19/0.77 fresh28(relation(c), true2, c, X)
% 0.19/0.77 = { by axiom 20 (fc4_funct_1) }
% 0.19/0.77 fresh27(function(c), true2, c, X)
% 0.19/0.77 = { by axiom 2 (t73_funct_1_2) }
% 0.19/0.77 fresh27(true2, true2, c, X)
% 0.19/0.77 = { by axiom 11 (fc4_funct_1) }
% 0.19/0.77 true2
% 0.19/0.77
% 0.19/0.77 Lemma 36: relation(relation_dom_restriction(c, X)) = true2.
% 0.19/0.77 Proof:
% 0.19/0.77 relation(relation_dom_restriction(c, X))
% 0.19/0.77 = { by axiom 19 (dt_k7_relat_1) R->L }
% 0.19/0.77 fresh35(relation(c), true2, c, X)
% 0.19/0.77 = { by axiom 1 (t73_funct_1_3) }
% 0.19/0.77 fresh35(true2, true2, c, X)
% 0.19/0.77 = { by axiom 9 (dt_k7_relat_1) }
% 0.19/0.77 true2
% 0.19/0.77
% 0.19/0.77 Goal 1 (t73_funct_1_4): in(apply(c, b), relation_rng(relation_dom_restriction(c, a))) = true2.
% 0.19/0.77 Proof:
% 0.19/0.77 in(apply(c, b), relation_rng(relation_dom_restriction(c, a)))
% 0.19/0.77 = { by axiom 13 (d5_funct_1_1) R->L }
% 0.19/0.77 fresh72(true2, true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by lemma 35 R->L }
% 0.19/0.77 fresh72(function(relation_dom_restriction(c, a)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 23 (d5_funct_1_1) R->L }
% 0.19/0.77 fresh71(true2, true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 8 (d5_funct_1_2) R->L }
% 0.19/0.77 fresh71(fresh37(apply(c, b), apply(c, b), relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 22 (t72_funct_1) R->L }
% 0.19/0.77 fresh71(fresh37(apply(c, b), fresh6(true2, true2, a, c, b), relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 3 (t73_funct_1_1) R->L }
% 0.19/0.77 fresh71(fresh37(apply(c, b), fresh6(in(b, a), true2, a, c, b), relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 32 (t72_funct_1) R->L }
% 0.19/0.77 fresh71(fresh37(apply(c, b), fresh52(relation(c), true2, a, c, b), relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 1 (t73_funct_1_3) }
% 0.19/0.77 fresh71(fresh37(apply(c, b), fresh52(true2, true2, a, c, b), relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 27 (t72_funct_1) }
% 0.19/0.77 fresh71(fresh37(apply(c, b), fresh53(function(c), true2, a, c, b), relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 2 (t73_funct_1_2) }
% 0.19/0.77 fresh71(fresh37(apply(c, b), fresh53(true2, true2, a, c, b), relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 15 (t72_funct_1) }
% 0.19/0.77 fresh71(fresh37(apply(c, b), apply(relation_dom_restriction(c, a), b), relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 33 (d5_funct_1_2) R->L }
% 0.19/0.77 fresh71(fresh38(in(b, relation_dom(relation_dom_restriction(c, a))), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 28 (d3_xboole_0_2) R->L }
% 0.19/0.77 fresh71(fresh38(fresh46(true2, true2, a, relation_dom(c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 17 (d3_xboole_0_3) R->L }
% 0.19/0.77 fresh71(fresh38(fresh46(fresh43(true2, true2, a, relation_dom(c), b), true2, a, relation_dom(c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 3 (t73_funct_1_1) R->L }
% 0.19/0.77 fresh71(fresh38(fresh46(fresh43(in(b, a), true2, a, relation_dom(c), b), true2, a, relation_dom(c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 30 (d3_xboole_0_3) R->L }
% 0.19/0.77 fresh71(fresh38(fresh46(fresh44(in(b, relation_dom(c)), true2, a, relation_dom(c), b), true2, a, relation_dom(c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 5 (t73_funct_1) }
% 0.19/0.77 fresh71(fresh38(fresh46(fresh44(true2, true2, a, relation_dom(c), b), true2, a, relation_dom(c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.77 = { by axiom 16 (d3_xboole_0_3) }
% 0.19/0.77 fresh71(fresh38(fresh46(equiv2(a, relation_dom(c), b), true2, a, relation_dom(c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 34 (d3_xboole_0_2) }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), set_intersection2(a, relation_dom(c)), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 4 (commutativity_k3_xboole_0) R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), set_intersection2(relation_dom(c), a), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 14 (t68_funct_1_1) R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh62(true2, true2, a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by lemma 35 R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh62(function(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 24 (t68_funct_1_1) R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh61(true2, true2, a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 2 (t73_funct_1_2) R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh61(function(c), true2, a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 25 (t68_funct_1_1) R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh60(true2, true2, a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by lemma 36 R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh60(relation(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 26 (t68_funct_1_1) R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh59(true2, true2, a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 1 (t73_funct_1_3) R->L }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh59(relation(c), true2, a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 31 (t68_funct_1_1) }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), fresh9(relation_dom_restriction(c, a), relation_dom_restriction(c, a), a, relation_dom_restriction(c, a), c), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 21 (t68_funct_1_1) }
% 0.19/0.78 fresh71(fresh38(fresh45(relation_dom(relation_dom_restriction(c, a)), relation_dom(relation_dom_restriction(c, a)), relation_dom(relation_dom_restriction(c, a)), b), true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 7 (d3_xboole_0_2) }
% 0.19/0.78 fresh71(fresh38(true2, true2, relation_dom_restriction(c, a), apply(c, b), b), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 18 (d5_funct_1_2) }
% 0.19/0.78 fresh71(equiv(relation_dom_restriction(c, a), apply(c, b)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 29 (d5_funct_1_1) }
% 0.19/0.78 fresh73(relation(relation_dom_restriction(c, a)), true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by lemma 36 }
% 0.19/0.78 fresh73(true2, true2, relation_dom_restriction(c, a), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 12 (d5_funct_1_1) }
% 0.19/0.78 fresh74(relation_rng(relation_dom_restriction(c, a)), relation_rng(relation_dom_restriction(c, a)), relation_rng(relation_dom_restriction(c, a)), apply(c, b))
% 0.19/0.78 = { by axiom 6 (d5_funct_1_1) }
% 0.19/0.78 true2
% 0.19/0.78 % SZS output end Proof
% 0.19/0.78
% 0.19/0.78 RESULT: Theorem (the conjecture is true).
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