TSTP Solution File: SEU037+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU037+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 13.29s 2.07s
% Output : Proof 13.39s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU037+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 13:16:00 EDT 2023
% 0.13/0.34 % CPUTime :
% 13.29/2.07 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 13.29/2.07
% 13.29/2.07 % SZS status Theorem
% 13.29/2.07
% 13.29/2.07 % SZS output start Proof
% 13.29/2.07 Take the following subset of the input axioms:
% 13.29/2.08 fof(dt_k7_relat_1, axiom, ![B, A2]: (relation(A2) => relation(relation_dom_restriction(A2, B)))).
% 13.29/2.08 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))))).
% 13.29/2.08 fof(t68_funct_1, axiom, ![B2, A2_2]: ((relation(B2) & function(B2)) => ![C]: ((relation(C) & function(C)) => (B2=relation_dom_restriction(C, A2_2) <=> (relation_dom(B2)=set_intersection2(relation_dom(C), A2_2) & ![D]: (in(D, relation_dom(B2)) => apply(B2, D)=apply(C, D))))))).
% 13.29/2.08 fof(t71_funct_1, conjecture, ![A, B2, C2]: ((relation(C2) & function(C2)) => (in(B2, set_intersection2(relation_dom(C2), A)) => apply(relation_dom_restriction(C2, A), B2)=apply(C2, B2)))).
% 13.29/2.08
% 13.29/2.08 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.29/2.08 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.29/2.08 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.29/2.08 fresh(y, y, x1...xn) = u
% 13.29/2.08 C => fresh(s, t, x1...xn) = v
% 13.29/2.08 where fresh is a fresh function symbol and x1..xn are the free
% 13.29/2.08 variables of u and v.
% 13.29/2.08 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.29/2.08 input problem has no model of domain size 1).
% 13.29/2.08
% 13.29/2.08 The encoding turns the above axioms into the following unit equations and goals:
% 13.29/2.08
% 13.39/2.08 Axiom 1 (t71_funct_1_2): relation(c) = true2.
% 13.39/2.08 Axiom 2 (t71_funct_1_1): function(c) = true2.
% 13.39/2.08 Axiom 3 (t71_funct_1): in(b, set_intersection2(relation_dom(c), a)) = true2.
% 13.39/2.08 Axiom 4 (dt_k7_relat_1): fresh27(X, X, Y, Z) = true2.
% 13.39/2.08 Axiom 5 (fc4_funct_1): fresh20(X, X, Y, Z) = function(relation_dom_restriction(Y, Z)).
% 13.39/2.08 Axiom 6 (fc4_funct_1): fresh19(X, X, Y, Z) = true2.
% 13.39/2.08 Axiom 7 (t68_funct_1_1): fresh39(X, X, Y, Z, W) = set_intersection2(relation_dom(W), Y).
% 13.39/2.08 Axiom 8 (t68_funct_1): fresh35(X, X, Y, Z, W) = apply(Z, W).
% 13.39/2.08 Axiom 9 (dt_k7_relat_1): fresh27(relation(X), true2, X, Y) = relation(relation_dom_restriction(X, Y)).
% 13.39/2.08 Axiom 10 (fc4_funct_1): fresh20(relation(X), true2, X, Y) = fresh19(function(X), true2, X, Y).
% 13.39/2.08 Axiom 11 (t68_funct_1_1): fresh5(X, X, Y, Z, W) = relation_dom(Z).
% 13.39/2.08 Axiom 12 (t68_funct_1_1): fresh38(X, X, Y, Z, W) = fresh39(function(Z), true2, Y, Z, W).
% 13.39/2.08 Axiom 13 (t68_funct_1_1): fresh37(X, X, Y, Z, W) = fresh38(function(W), true2, Y, Z, W).
% 13.39/2.08 Axiom 14 (t68_funct_1_1): fresh36(X, X, Y, Z, W) = fresh37(relation(Z), true2, Y, Z, W).
% 13.39/2.08 Axiom 15 (t68_funct_1): fresh34(X, X, Y, Z, W, V) = fresh35(Z, relation_dom_restriction(W, Y), Z, W, V).
% 13.39/2.08 Axiom 16 (t68_funct_1): fresh6(X, X, Y, Z, W, V) = apply(Z, V).
% 13.39/2.08 Axiom 17 (t68_funct_1_1): fresh36(relation(X), true2, Y, Z, X) = fresh5(Z, relation_dom_restriction(X, Y), Y, Z, X).
% 13.39/2.08 Axiom 18 (t68_funct_1): fresh33(X, X, Y, Z, W, V) = fresh34(function(Z), true2, Y, Z, W, V).
% 13.39/2.08 Axiom 19 (t68_funct_1): fresh32(X, X, Y, Z, W, V) = fresh33(function(W), true2, Y, Z, W, V).
% 13.39/2.08 Axiom 20 (t68_funct_1): fresh31(X, X, Y, Z, W, V) = fresh32(relation(Z), true2, Y, Z, W, V).
% 13.39/2.08 Axiom 21 (t68_funct_1): fresh31(relation(X), true2, Y, Z, X, W) = fresh6(in(W, relation_dom(Z)), true2, Y, Z, X, W).
% 13.39/2.08
% 13.39/2.08 Lemma 22: relation(relation_dom_restriction(c, X)) = true2.
% 13.39/2.08 Proof:
% 13.39/2.08 relation(relation_dom_restriction(c, X))
% 13.39/2.08 = { by axiom 9 (dt_k7_relat_1) R->L }
% 13.39/2.08 fresh27(relation(c), true2, c, X)
% 13.39/2.08 = { by axiom 1 (t71_funct_1_2) }
% 13.39/2.08 fresh27(true2, true2, c, X)
% 13.39/2.08 = { by axiom 4 (dt_k7_relat_1) }
% 13.39/2.08 true2
% 13.39/2.08
% 13.39/2.08 Lemma 23: function(relation_dom_restriction(c, X)) = true2.
% 13.39/2.08 Proof:
% 13.39/2.08 function(relation_dom_restriction(c, X))
% 13.39/2.08 = { by axiom 5 (fc4_funct_1) R->L }
% 13.39/2.08 fresh20(true2, true2, c, X)
% 13.39/2.08 = { by axiom 1 (t71_funct_1_2) R->L }
% 13.39/2.08 fresh20(relation(c), true2, c, X)
% 13.39/2.08 = { by axiom 10 (fc4_funct_1) }
% 13.39/2.08 fresh19(function(c), true2, c, X)
% 13.39/2.08 = { by axiom 2 (t71_funct_1_1) }
% 13.39/2.08 fresh19(true2, true2, c, X)
% 13.39/2.08 = { by axiom 6 (fc4_funct_1) }
% 13.39/2.08 true2
% 13.39/2.08
% 13.39/2.08 Goal 1 (t71_funct_1_3): apply(relation_dom_restriction(c, a), b) = apply(c, b).
% 13.39/2.08 Proof:
% 13.39/2.08 apply(relation_dom_restriction(c, a), b)
% 13.39/2.08 = { by axiom 16 (t68_funct_1) R->L }
% 13.39/2.08 fresh6(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 3 (t71_funct_1) R->L }
% 13.39/2.08 fresh6(in(b, set_intersection2(relation_dom(c), a)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 7 (t68_funct_1_1) R->L }
% 13.39/2.08 fresh6(in(b, fresh39(true2, true2, a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by lemma 23 R->L }
% 13.39/2.08 fresh6(in(b, fresh39(function(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 12 (t68_funct_1_1) R->L }
% 13.39/2.08 fresh6(in(b, fresh38(true2, true2, a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 2 (t71_funct_1_1) R->L }
% 13.39/2.08 fresh6(in(b, fresh38(function(c), true2, a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 13 (t68_funct_1_1) R->L }
% 13.39/2.08 fresh6(in(b, fresh37(true2, true2, a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by lemma 22 R->L }
% 13.39/2.08 fresh6(in(b, fresh37(relation(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 14 (t68_funct_1_1) R->L }
% 13.39/2.08 fresh6(in(b, fresh36(true2, true2, a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 1 (t71_funct_1_2) R->L }
% 13.39/2.08 fresh6(in(b, fresh36(relation(c), true2, a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 17 (t68_funct_1_1) }
% 13.39/2.08 fresh6(in(b, fresh5(relation_dom_restriction(c, a), relation_dom_restriction(c, a), a, relation_dom_restriction(c, a), c)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 11 (t68_funct_1_1) }
% 13.39/2.08 fresh6(in(b, relation_dom(relation_dom_restriction(c, a))), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 21 (t68_funct_1) R->L }
% 13.39/2.08 fresh31(relation(c), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 1 (t71_funct_1_2) }
% 13.39/2.08 fresh31(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 20 (t68_funct_1) }
% 13.39/2.08 fresh32(relation(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by lemma 22 }
% 13.39/2.08 fresh32(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 19 (t68_funct_1) }
% 13.39/2.08 fresh33(function(c), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 2 (t71_funct_1_1) }
% 13.39/2.08 fresh33(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 18 (t68_funct_1) }
% 13.39/2.08 fresh34(function(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by lemma 23 }
% 13.39/2.08 fresh34(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 15 (t68_funct_1) }
% 13.39/2.08 fresh35(relation_dom_restriction(c, a), relation_dom_restriction(c, a), relation_dom_restriction(c, a), c, b)
% 13.39/2.08 = { by axiom 8 (t68_funct_1) }
% 13.39/2.08 apply(c, b)
% 13.39/2.08 % SZS output end Proof
% 13.39/2.08
% 13.39/2.08 RESULT: Theorem (the conjecture is true).
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