TSTP Solution File: SEU139+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : SEU139+1 : 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 : n017.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 17:51:09 EDT 2023
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% 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 : SEU139+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 16:17:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.39 Command-line arguments: --flatten
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 Take the following subset of the input axioms:
% 0.14/0.40 fof(antisymmetry_r2_xboole_0, axiom, ![A, B]: (proper_subset(A, B) => ~proper_subset(B, A))).
% 0.14/0.40 fof(d10_xboole_0, axiom, ![A2, B2]: (A2=B2 <=> (subset(A2, B2) & subset(B2, A2)))).
% 0.14/0.40 fof(d8_xboole_0, axiom, ![B2, A2_2]: (proper_subset(A2_2, B2) <=> (subset(A2_2, B2) & A2_2!=B2))).
% 0.14/0.40 fof(irreflexivity_r2_xboole_0, axiom, ![A3, B2]: ~proper_subset(A3, A3)).
% 0.14/0.40 fof(t60_xboole_1, conjecture, ![A3, B2]: ~(subset(A3, B2) & proper_subset(B2, A3))).
% 0.14/0.40
% 0.14/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.40 fresh(y, y, x1...xn) = u
% 0.14/0.40 C => fresh(s, t, x1...xn) = v
% 0.14/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.40 variables of u and v.
% 0.14/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.40 input problem has no model of domain size 1).
% 0.14/0.40
% 0.14/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.40
% 0.14/0.40 Axiom 1 (t60_xboole_1): proper_subset(b, a) = true2.
% 0.14/0.40 Axiom 2 (t60_xboole_1_1): subset(a, b) = true2.
% 0.14/0.40 Axiom 3 (d10_xboole_0_1): fresh(X, X, Y, Z) = Z.
% 0.14/0.40 Axiom 4 (d10_xboole_0_1): fresh3(X, X, Y, Z) = Y.
% 0.14/0.40 Axiom 5 (d8_xboole_0): fresh2(X, X, Y, Z) = true2.
% 0.14/0.40 Axiom 6 (d10_xboole_0_1): fresh3(subset(X, Y), true2, Y, X) = fresh(subset(Y, X), true2, Y, X).
% 0.14/0.40 Axiom 7 (d8_xboole_0): fresh2(proper_subset(X, Y), true2, X, Y) = subset(X, Y).
% 0.14/0.40
% 0.14/0.40 Goal 1 (d8_xboole_0_1): proper_subset(X, X) = true2.
% 0.14/0.40 The goal is true when:
% 0.14/0.40 X = a
% 0.14/0.40
% 0.14/0.40 Proof:
% 0.14/0.40 proper_subset(a, a)
% 0.14/0.40 = { by axiom 4 (d10_xboole_0_1) R->L }
% 0.14/0.40 proper_subset(fresh3(proper_subset(b, a), proper_subset(b, a), a, b), a)
% 0.14/0.40 = { by axiom 1 (t60_xboole_1) }
% 0.14/0.40 proper_subset(fresh3(true2, proper_subset(b, a), a, b), a)
% 0.14/0.40 = { by axiom 5 (d8_xboole_0) R->L }
% 0.14/0.40 proper_subset(fresh3(fresh2(proper_subset(b, a), proper_subset(b, a), b, a), proper_subset(b, a), a, b), a)
% 0.14/0.40 = { by axiom 1 (t60_xboole_1) }
% 0.14/0.40 proper_subset(fresh3(fresh2(proper_subset(b, a), true2, b, a), proper_subset(b, a), a, b), a)
% 0.14/0.40 = { by axiom 7 (d8_xboole_0) }
% 0.14/0.40 proper_subset(fresh3(subset(b, a), proper_subset(b, a), a, b), a)
% 0.14/0.40 = { by axiom 1 (t60_xboole_1) }
% 0.14/0.40 proper_subset(fresh3(subset(b, a), true2, a, b), a)
% 0.14/0.40 = { by axiom 6 (d10_xboole_0_1) }
% 0.14/0.40 proper_subset(fresh(subset(a, b), true2, a, b), a)
% 0.14/0.40 = { by axiom 1 (t60_xboole_1) R->L }
% 0.14/0.40 proper_subset(fresh(subset(a, b), proper_subset(b, a), a, b), a)
% 0.14/0.40 = { by axiom 2 (t60_xboole_1_1) }
% 0.14/0.40 proper_subset(fresh(true2, proper_subset(b, a), a, b), a)
% 0.14/0.40 = { by axiom 1 (t60_xboole_1) R->L }
% 0.14/0.40 proper_subset(fresh(proper_subset(b, a), proper_subset(b, a), a, b), a)
% 0.14/0.40 = { by axiom 3 (d10_xboole_0_1) }
% 0.14/0.40 proper_subset(b, a)
% 0.14/0.40 = { by axiom 1 (t60_xboole_1) }
% 0.14/0.40 true2
% 0.14/0.40 % SZS output end Proof
% 0.14/0.40
% 0.14/0.40 RESULT: Theorem (the conjecture is true).
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