TSTP Solution File: SEU223+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n010.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 17:51:39 EDT 2023
% Result : Theorem 112.53s 14.77s
% Output : Proof 112.53s
% 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 : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n010.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 15:08:36 EDT 2023
% 0.13/0.35 % CPUTime :
% 112.53/14.77 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 112.53/14.77
% 112.53/14.77 % SZS status Theorem
% 112.53/14.77
% 112.53/14.78 % SZS output start Proof
% 112.53/14.78 Take the following subset of the input axioms:
% 112.53/14.78 fof(dt_k7_relat_1, axiom, ![B, A2]: (relation(A2) => relation(relation_dom_restriction(A2, B)))).
% 112.53/14.78 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))))).
% 112.53/14.78 fof(t68_funct_1, lemma, ![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))))))).
% 112.53/14.78 fof(t70_funct_1, conjecture, ![A, B2, C2]: ((relation(C2) & function(C2)) => (in(B2, relation_dom(relation_dom_restriction(C2, A))) => apply(relation_dom_restriction(C2, A), B2)=apply(C2, B2)))).
% 112.53/14.78
% 112.53/14.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 112.53/14.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 112.53/14.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 112.53/14.78 fresh(y, y, x1...xn) = u
% 112.53/14.78 C => fresh(s, t, x1...xn) = v
% 112.53/14.78 where fresh is a fresh function symbol and x1..xn are the free
% 112.53/14.78 variables of u and v.
% 112.53/14.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 112.53/14.78 input problem has no model of domain size 1).
% 112.53/14.78
% 112.53/14.78 The encoding turns the above axioms into the following unit equations and goals:
% 112.53/14.78
% 112.53/14.78 Axiom 1 (t70_funct_1_2): relation(c) = true2.
% 112.53/14.78 Axiom 2 (t70_funct_1_1): function(c) = true2.
% 112.53/14.78 Axiom 3 (t70_funct_1): in(b2, relation_dom(relation_dom_restriction(c, a))) = true2.
% 112.53/14.78 Axiom 4 (dt_k7_relat_1): fresh241(X, X, Y, Z) = true2.
% 112.53/14.78 Axiom 5 (fc4_funct_1): fresh220(X, X, Y, Z) = function(relation_dom_restriction(Y, Z)).
% 112.53/14.78 Axiom 6 (fc4_funct_1): fresh219(X, X, Y, Z) = true2.
% 112.53/14.78 Axiom 7 (t68_funct_1): fresh386(X, X, Y, Z, W) = apply(Z, W).
% 112.53/14.78 Axiom 8 (dt_k7_relat_1): fresh241(relation(X), true2, X, Y) = relation(relation_dom_restriction(X, Y)).
% 112.53/14.78 Axiom 9 (fc4_funct_1): fresh220(relation(X), true2, X, Y) = fresh219(function(X), true2, X, Y).
% 112.53/14.78 Axiom 10 (t68_funct_1): fresh385(X, X, Y, Z, W, V) = fresh386(Z, relation_dom_restriction(W, Y), Z, W, V).
% 112.53/14.78 Axiom 11 (t68_funct_1): fresh82(X, X, Y, Z, W, V) = apply(Z, V).
% 112.53/14.78 Axiom 12 (t68_funct_1): fresh384(X, X, Y, Z, W, V) = fresh385(function(Z), true2, Y, Z, W, V).
% 112.53/14.78 Axiom 13 (t68_funct_1): fresh383(X, X, Y, Z, W, V) = fresh384(function(W), true2, Y, Z, W, V).
% 112.53/14.78 Axiom 14 (t68_funct_1): fresh382(X, X, Y, Z, W, V) = fresh383(relation(Z), true2, Y, Z, W, V).
% 112.53/14.78 Axiom 15 (t68_funct_1): fresh382(relation(X), true2, Y, Z, X, W) = fresh82(in(W, relation_dom(Z)), true2, Y, Z, X, W).
% 112.53/14.78
% 112.53/14.78 Goal 1 (t70_funct_1_3): apply(relation_dom_restriction(c, a), b2) = apply(c, b2).
% 112.53/14.78 Proof:
% 112.53/14.78 apply(relation_dom_restriction(c, a), b2)
% 112.53/14.78 = { by axiom 11 (t68_funct_1) R->L }
% 112.53/14.78 fresh82(true2, true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 3 (t70_funct_1) R->L }
% 112.53/14.78 fresh82(in(b2, relation_dom(relation_dom_restriction(c, a))), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 15 (t68_funct_1) R->L }
% 112.53/14.78 fresh382(relation(c), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 1 (t70_funct_1_2) }
% 112.53/14.78 fresh382(true2, true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 14 (t68_funct_1) }
% 112.53/14.78 fresh383(relation(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 8 (dt_k7_relat_1) R->L }
% 112.53/14.78 fresh383(fresh241(relation(c), true2, c, a), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 1 (t70_funct_1_2) }
% 112.53/14.78 fresh383(fresh241(true2, true2, c, a), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 4 (dt_k7_relat_1) }
% 112.53/14.78 fresh383(true2, true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 13 (t68_funct_1) }
% 112.53/14.78 fresh384(function(c), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 2 (t70_funct_1_1) }
% 112.53/14.78 fresh384(true2, true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 12 (t68_funct_1) }
% 112.53/14.78 fresh385(function(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 5 (fc4_funct_1) R->L }
% 112.53/14.78 fresh385(fresh220(true2, true2, c, a), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 1 (t70_funct_1_2) R->L }
% 112.53/14.78 fresh385(fresh220(relation(c), true2, c, a), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 9 (fc4_funct_1) }
% 112.53/14.78 fresh385(fresh219(function(c), true2, c, a), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 2 (t70_funct_1_1) }
% 112.53/14.78 fresh385(fresh219(true2, true2, c, a), true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 6 (fc4_funct_1) }
% 112.53/14.78 fresh385(true2, true2, a, relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 10 (t68_funct_1) }
% 112.53/14.78 fresh386(relation_dom_restriction(c, a), relation_dom_restriction(c, a), relation_dom_restriction(c, a), c, b2)
% 112.53/14.78 = { by axiom 7 (t68_funct_1) }
% 112.53/14.78 apply(c, b2)
% 112.53/14.78 % SZS output end Proof
% 112.53/14.78
% 112.53/14.78 RESULT: Theorem (the conjecture is true).
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