TSTP Solution File: HEN005-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : HEN005-3 : TPTP v8.1.2. Released v1.0.0.
% 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 : n018.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 01:56:54 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% 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 : HEN005-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 13:36:42 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.39 Command-line arguments: --no-flatten-goal
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% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Take the following subset of the input axioms:
% 0.20/0.40 fof(a_LE_b, hypothesis, less_equal(a, b)).
% 0.20/0.40 fof(b_LE_c, hypothesis, less_equal(b, c)).
% 0.20/0.40 fof(less_equal_and_equal, axiom, ![X, Y]: (~less_equal(X, Y) | (~less_equal(Y, X) | X=Y))).
% 0.20/0.40 fof(prove_a_LE_c, negated_conjecture, ~less_equal(a, c)).
% 0.20/0.40 fof(quotient_less_equal1, axiom, ![X2, Y2]: (~less_equal(X2, Y2) | divide(X2, Y2)=zero)).
% 0.20/0.40 fof(quotient_less_equal2, axiom, ![X2, Y2]: (divide(X2, Y2)!=zero | less_equal(X2, Y2))).
% 0.20/0.41 fof(quotient_property, axiom, ![Z, X2, Y2]: less_equal(divide(divide(X2, Z), divide(Y2, Z)), divide(divide(X2, Y2), Z))).
% 0.20/0.41 fof(zero_is_smallest, axiom, ![X2]: less_equal(zero, X2)).
% 0.20/0.41
% 0.20/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.41 fresh(y, y, x1...xn) = u
% 0.20/0.41 C => fresh(s, t, x1...xn) = v
% 0.20/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.41 variables of u and v.
% 0.20/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.41 input problem has no model of domain size 1).
% 0.20/0.41
% 0.20/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.41
% 0.20/0.41 Axiom 1 (a_LE_b): less_equal(a, b) = true.
% 0.20/0.41 Axiom 2 (b_LE_c): less_equal(b, c) = true.
% 0.20/0.41 Axiom 3 (zero_is_smallest): less_equal(zero, X) = true.
% 0.20/0.41 Axiom 4 (less_equal_and_equal): fresh(X, X, Y, Z) = Z.
% 0.20/0.41 Axiom 5 (quotient_less_equal2): fresh4(X, X, Y, Z) = true.
% 0.20/0.41 Axiom 6 (quotient_less_equal1): fresh3(X, X, Y, Z) = zero.
% 0.20/0.41 Axiom 7 (less_equal_and_equal): fresh2(X, X, Y, Z) = Y.
% 0.20/0.41 Axiom 8 (quotient_less_equal2): fresh4(divide(X, Y), zero, X, Y) = less_equal(X, Y).
% 0.20/0.41 Axiom 9 (quotient_less_equal1): fresh3(less_equal(X, Y), true, X, Y) = divide(X, Y).
% 0.20/0.41 Axiom 10 (less_equal_and_equal): fresh2(less_equal(X, Y), true, Y, X) = fresh(less_equal(Y, X), true, Y, X).
% 0.20/0.41 Axiom 11 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_a_LE_c): less_equal(a, c) = true.
% 0.20/0.41 Proof:
% 0.20/0.41 less_equal(a, c)
% 0.20/0.41 = { by axiom 8 (quotient_less_equal2) R->L }
% 0.20/0.41 fresh4(divide(a, c), zero, a, c)
% 0.20/0.41 = { by axiom 4 (less_equal_and_equal) R->L }
% 0.20/0.41 fresh4(fresh(true, true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 3 (zero_is_smallest) R->L }
% 0.20/0.41 fresh4(fresh(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 10 (less_equal_and_equal) R->L }
% 0.20/0.41 fresh4(fresh2(less_equal(divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 8 (quotient_less_equal2) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(divide(divide(a, c), zero), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 6 (quotient_less_equal1) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(divide(divide(a, c), fresh3(true, true, b, c)), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 2 (b_LE_c) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(divide(divide(a, c), fresh3(less_equal(b, c), true, b, c)), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 9 (quotient_less_equal1) }
% 0.20/0.41 fresh4(fresh2(fresh4(divide(divide(a, c), divide(b, c)), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 4 (less_equal_and_equal) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh(true, true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 3 (zero_is_smallest) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 10 (less_equal_and_equal) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), divide(b, c)), zero), true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 6 (quotient_less_equal1) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), divide(b, c)), fresh3(true, true, zero, c)), true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 3 (zero_is_smallest) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), divide(b, c)), fresh3(less_equal(zero, c), true, zero, c)), true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 9 (quotient_less_equal1) }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), divide(b, c)), divide(zero, c)), true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 6 (quotient_less_equal1) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), divide(b, c)), divide(fresh3(true, true, a, b), c)), true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 1 (a_LE_b) R->L }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), divide(b, c)), divide(fresh3(less_equal(a, b), true, a, b), c)), true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 9 (quotient_less_equal1) }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), divide(b, c)), divide(divide(a, b), c)), true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 11 (quotient_property) }
% 0.20/0.41 fresh4(fresh2(fresh4(fresh2(true, true, zero, divide(divide(a, c), divide(b, c))), zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 7 (less_equal_and_equal) }
% 0.20/0.41 fresh4(fresh2(fresh4(zero, zero, divide(a, c), zero), true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 5 (quotient_less_equal2) }
% 0.20/0.41 fresh4(fresh2(true, true, zero, divide(a, c)), zero, a, c)
% 0.20/0.41 = { by axiom 7 (less_equal_and_equal) }
% 0.20/0.41 fresh4(zero, zero, a, c)
% 0.20/0.41 = { by axiom 5 (quotient_less_equal2) }
% 0.20/0.41 true
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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