TSTP Solution File: SEU080+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU080+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 : n015.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 17:50:57 EDT 2023
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% 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 : SEU080+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
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 20:25:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.46 Command-line arguments: --no-flatten-goal
% 0.19/0.46
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 Take the following subset of the input axioms:
% 0.19/0.47 fof(d10_xboole_0, axiom, ![B, A2]: (A2=B <=> (subset(A2, B) & subset(B, A2)))).
% 0.19/0.47 fof(t158_funct_1, axiom, ![C, B2, A2_2]: ((relation(C) & function(C)) => ((subset(relation_inverse_image(C, A2_2), relation_inverse_image(C, B2)) & subset(A2_2, relation_rng(C))) => subset(A2_2, B2)))).
% 0.19/0.47 fof(t161_funct_1, conjecture, ![A, B2, C2]: ((relation(C2) & function(C2)) => ((relation_inverse_image(C2, A)=relation_inverse_image(C2, B2) & (subset(A, relation_rng(C2)) & subset(B2, relation_rng(C2)))) => A=B2))).
% 0.19/0.47
% 0.19/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.47 fresh(y, y, x1...xn) = u
% 0.19/0.47 C => fresh(s, t, x1...xn) = v
% 0.19/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.47 variables of u and v.
% 0.19/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.47 input problem has no model of domain size 1).
% 0.19/0.47
% 0.19/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.47
% 0.19/0.47 Axiom 1 (t161_funct_1_1): function(c) = true2.
% 0.19/0.47 Axiom 2 (t161_funct_1_2): relation(c) = true2.
% 0.19/0.47 Axiom 3 (t161_funct_1): relation_inverse_image(c, a) = relation_inverse_image(c, b).
% 0.19/0.47 Axiom 4 (d10_xboole_0): subset(X, X) = true2.
% 0.19/0.47 Axiom 5 (t161_funct_1_3): subset(b, relation_rng(c)) = true2.
% 0.19/0.47 Axiom 6 (t161_funct_1_4): subset(a, relation_rng(c)) = true2.
% 0.19/0.47 Axiom 7 (t158_funct_1): fresh22(X, X, Y, Z) = true2.
% 0.19/0.47 Axiom 8 (d10_xboole_0_1): fresh4(X, X, Y, Z) = Y.
% 0.19/0.47 Axiom 9 (d10_xboole_0_1): fresh3(X, X, Y, Z) = Z.
% 0.19/0.47 Axiom 10 (t158_funct_1): fresh21(X, X, Y, Z, W) = fresh22(function(W), true2, Y, Z).
% 0.19/0.47 Axiom 11 (t158_funct_1): fresh20(X, X, Y, Z, W) = subset(Y, Z).
% 0.19/0.47 Axiom 12 (t158_funct_1): fresh19(X, X, Y, Z, W) = fresh20(relation(W), true2, Y, Z, W).
% 0.19/0.47 Axiom 13 (d10_xboole_0_1): fresh4(subset(X, Y), true2, Y, X) = fresh3(subset(Y, X), true2, Y, X).
% 0.19/0.47 Axiom 14 (t158_funct_1): fresh19(subset(relation_inverse_image(X, Y), relation_inverse_image(X, Z)), true2, Y, Z, X) = fresh21(subset(Y, relation_rng(X)), true2, Y, Z, X).
% 0.19/0.47
% 0.19/0.47 Lemma 15: fresh19(X, X, Y, Z, c) = subset(Y, Z).
% 0.19/0.47 Proof:
% 0.19/0.47 fresh19(X, X, Y, Z, c)
% 0.19/0.47 = { by axiom 12 (t158_funct_1) }
% 0.19/0.47 fresh20(relation(c), true2, Y, Z, c)
% 0.19/0.47 = { by axiom 2 (t161_funct_1_2) }
% 0.19/0.47 fresh20(true2, true2, Y, Z, c)
% 0.19/0.47 = { by axiom 11 (t158_funct_1) }
% 0.19/0.47 subset(Y, Z)
% 0.19/0.47
% 0.19/0.47 Goal 1 (t161_funct_1_5): a = b.
% 0.19/0.47 Proof:
% 0.19/0.47 a
% 0.19/0.47 = { by axiom 9 (d10_xboole_0_1) R->L }
% 0.19/0.47 fresh3(true2, true2, b, a)
% 0.19/0.47 = { by axiom 7 (t158_funct_1) R->L }
% 0.19/0.47 fresh3(fresh22(true2, true2, b, a), true2, b, a)
% 0.19/0.47 = { by axiom 1 (t161_funct_1_1) R->L }
% 0.19/0.47 fresh3(fresh22(function(c), true2, b, a), true2, b, a)
% 0.19/0.47 = { by axiom 10 (t158_funct_1) R->L }
% 0.19/0.47 fresh3(fresh21(true2, true2, b, a, c), true2, b, a)
% 0.19/0.47 = { by axiom 5 (t161_funct_1_3) R->L }
% 0.19/0.47 fresh3(fresh21(subset(b, relation_rng(c)), true2, b, a, c), true2, b, a)
% 0.19/0.47 = { by axiom 14 (t158_funct_1) R->L }
% 0.19/0.47 fresh3(fresh19(subset(relation_inverse_image(c, b), relation_inverse_image(c, a)), true2, b, a, c), true2, b, a)
% 0.19/0.47 = { by axiom 3 (t161_funct_1) }
% 0.19/0.47 fresh3(fresh19(subset(relation_inverse_image(c, b), relation_inverse_image(c, b)), true2, b, a, c), true2, b, a)
% 0.19/0.47 = { by axiom 4 (d10_xboole_0) }
% 0.19/0.47 fresh3(fresh19(true2, true2, b, a, c), true2, b, a)
% 0.19/0.47 = { by lemma 15 }
% 0.19/0.47 fresh3(subset(b, a), true2, b, a)
% 0.19/0.47 = { by axiom 13 (d10_xboole_0_1) R->L }
% 0.19/0.47 fresh4(subset(a, b), true2, b, a)
% 0.19/0.47 = { by lemma 15 R->L }
% 0.19/0.47 fresh4(fresh19(true2, true2, a, b, c), true2, b, a)
% 0.19/0.47 = { by axiom 4 (d10_xboole_0) R->L }
% 0.19/0.47 fresh4(fresh19(subset(relation_inverse_image(c, b), relation_inverse_image(c, b)), true2, a, b, c), true2, b, a)
% 0.19/0.47 = { by axiom 3 (t161_funct_1) R->L }
% 0.19/0.47 fresh4(fresh19(subset(relation_inverse_image(c, a), relation_inverse_image(c, b)), true2, a, b, c), true2, b, a)
% 0.19/0.47 = { by axiom 14 (t158_funct_1) }
% 0.19/0.47 fresh4(fresh21(subset(a, relation_rng(c)), true2, a, b, c), true2, b, a)
% 0.19/0.47 = { by axiom 6 (t161_funct_1_4) }
% 0.19/0.47 fresh4(fresh21(true2, true2, a, b, c), true2, b, a)
% 0.19/0.47 = { by axiom 10 (t158_funct_1) }
% 0.19/0.47 fresh4(fresh22(function(c), true2, a, b), true2, b, a)
% 0.19/0.47 = { by axiom 1 (t161_funct_1_1) }
% 0.19/0.47 fresh4(fresh22(true2, true2, a, b), true2, b, a)
% 0.19/0.47 = { by axiom 7 (t158_funct_1) }
% 0.19/0.47 fresh4(true2, true2, b, a)
% 0.19/0.47 = { by axiom 8 (d10_xboole_0_1) }
% 0.19/0.47 b
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47
% 0.19/0.47 RESULT: Theorem (the conjecture is true).
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