TSTP Solution File: SEU097+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU097+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 : n009.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 17:51:00 EDT 2023
% Result : Theorem 20.38s 3.00s
% Output : Proof 20.38s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU097+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
% 0.11/0.34 % Computer : n009.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Wed Aug 23 13:08:06 EDT 2023
% 0.11/0.34 % CPUTime :
% 20.38/3.00 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 20.38/3.00
% 20.38/3.00 % SZS status Theorem
% 20.38/3.00
% 20.38/3.01 % SZS output start Proof
% 20.38/3.01 Take the following subset of the input axioms:
% 20.38/3.01 fof(commutativity_k5_xboole_0, axiom, ![A, B]: symmetric_difference(A, B)=symmetric_difference(B, A)).
% 20.38/3.01 fof(d6_xboole_0, axiom, ![A3, B2]: symmetric_difference(A3, B2)=set_union2(set_difference(A3, B2), set_difference(B2, A3))).
% 20.38/3.01 fof(fc12_finset_1, axiom, ![A2, B2]: (finite(A2) => finite(set_difference(A2, B2)))).
% 20.38/3.01 fof(fc9_finset_1, axiom, ![B2, A2_2]: ((finite(A2_2) & finite(B2)) => finite(set_union2(A2_2, B2)))).
% 20.38/3.01 fof(t28_finset_1, conjecture, ![A3, B2]: ((finite(A3) & finite(B2)) => finite(symmetric_difference(A3, B2)))).
% 20.38/3.01
% 20.38/3.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 20.38/3.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 20.38/3.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 20.38/3.01 fresh(y, y, x1...xn) = u
% 20.38/3.01 C => fresh(s, t, x1...xn) = v
% 20.38/3.01 where fresh is a fresh function symbol and x1..xn are the free
% 20.38/3.01 variables of u and v.
% 20.38/3.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 20.38/3.01 input problem has no model of domain size 1).
% 20.38/3.01
% 20.38/3.01 The encoding turns the above axioms into the following unit equations and goals:
% 20.38/3.01
% 20.38/3.01 Axiom 1 (t28_finset_1): finite(b) = true2.
% 20.38/3.01 Axiom 2 (t28_finset_1_1): finite(a) = true2.
% 20.38/3.01 Axiom 3 (commutativity_k5_xboole_0): symmetric_difference(X, Y) = symmetric_difference(Y, X).
% 20.38/3.01 Axiom 4 (d6_xboole_0): symmetric_difference(X, Y) = set_union2(set_difference(X, Y), set_difference(Y, X)).
% 20.38/3.01 Axiom 5 (fc12_finset_1): fresh22(X, X, Y, Z) = true2.
% 20.38/3.01 Axiom 6 (fc9_finset_1): fresh15(X, X, Y, Z) = finite(set_union2(Y, Z)).
% 20.38/3.01 Axiom 7 (fc9_finset_1): fresh14(X, X, Y, Z) = true2.
% 20.38/3.01 Axiom 8 (fc12_finset_1): fresh22(finite(X), true2, X, Y) = finite(set_difference(X, Y)).
% 20.38/3.01 Axiom 9 (fc9_finset_1): fresh15(finite(X), true2, Y, X) = fresh14(finite(Y), true2, Y, X).
% 20.38/3.01
% 20.38/3.01 Goal 1 (t28_finset_1_2): finite(symmetric_difference(a, b)) = true2.
% 20.38/3.01 Proof:
% 20.38/3.01 finite(symmetric_difference(a, b))
% 20.38/3.01 = { by axiom 3 (commutativity_k5_xboole_0) }
% 20.38/3.01 finite(symmetric_difference(b, a))
% 20.38/3.01 = { by axiom 4 (d6_xboole_0) }
% 20.38/3.01 finite(set_union2(set_difference(b, a), set_difference(a, b)))
% 20.38/3.01 = { by axiom 6 (fc9_finset_1) R->L }
% 20.38/3.01 fresh15(true2, true2, set_difference(b, a), set_difference(a, b))
% 20.38/3.01 = { by axiom 5 (fc12_finset_1) R->L }
% 20.38/3.01 fresh15(fresh22(true2, true2, a, b), true2, set_difference(b, a), set_difference(a, b))
% 20.38/3.01 = { by axiom 2 (t28_finset_1_1) R->L }
% 20.38/3.01 fresh15(fresh22(finite(a), true2, a, b), true2, set_difference(b, a), set_difference(a, b))
% 20.38/3.01 = { by axiom 8 (fc12_finset_1) }
% 20.38/3.01 fresh15(finite(set_difference(a, b)), true2, set_difference(b, a), set_difference(a, b))
% 20.38/3.01 = { by axiom 9 (fc9_finset_1) }
% 20.38/3.01 fresh14(finite(set_difference(b, a)), true2, set_difference(b, a), set_difference(a, b))
% 20.38/3.01 = { by axiom 8 (fc12_finset_1) R->L }
% 20.38/3.01 fresh14(fresh22(finite(b), true2, b, a), true2, set_difference(b, a), set_difference(a, b))
% 20.38/3.01 = { by axiom 1 (t28_finset_1) }
% 20.38/3.01 fresh14(fresh22(true2, true2, b, a), true2, set_difference(b, a), set_difference(a, b))
% 20.38/3.01 = { by axiom 5 (fc12_finset_1) }
% 20.38/3.01 fresh14(true2, true2, set_difference(b, a), set_difference(a, b))
% 20.38/3.01 = { by axiom 7 (fc9_finset_1) }
% 20.38/3.01 true2
% 20.38/3.01 % SZS output end Proof
% 20.38/3.01
% 20.38/3.01 RESULT: Theorem (the conjecture is true).
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