TSTP Solution File: HEN004-5 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : HEN004-5 : 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 : n011.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 01:56:53 EDT 2023
% Result : Unsatisfiable 0.20s 0.38s
% 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
% 0.07/0.12 % Problem : HEN004-5 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % 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 : n011.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 : Thu Aug 24 13:29:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
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% 0.20/0.38 % SZS status Unsatisfiable
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% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 Take the following subset of the input axioms:
% 0.20/0.39 fof(divide_and_equal, axiom, ![X, Y]: (divide(X, Y)!=zero | (divide(Y, X)!=zero | X=Y))).
% 0.20/0.39 fof(prove_x_divide_zero_is_x, negated_conjecture, divide(a, zero)!=a).
% 0.20/0.39 fof(quotient_property, axiom, ![Z, X2, Y2]: divide(divide(divide(X2, Z), divide(Y2, Z)), divide(divide(X2, Y2), Z))=zero).
% 0.20/0.39 fof(quotient_smaller_than_numerator, axiom, ![X2, Y2]: divide(divide(X2, Y2), X2)=zero).
% 0.20/0.39 fof(x_divide_x_is_zero, axiom, ![X2]: divide(X2, X2)=zero).
% 0.20/0.39 fof(zero_is_smallest, axiom, ![X2]: divide(zero, X2)=zero).
% 0.20/0.39
% 0.20/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.39 fresh(y, y, x1...xn) = u
% 0.20/0.39 C => fresh(s, t, x1...xn) = v
% 0.20/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.39 variables of u and v.
% 0.20/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.39 input problem has no model of domain size 1).
% 0.20/0.39
% 0.20/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.39
% 0.20/0.39 Axiom 1 (x_divide_x_is_zero): divide(X, X) = zero.
% 0.20/0.39 Axiom 2 (zero_is_smallest): divide(zero, X) = zero.
% 0.20/0.39 Axiom 3 (divide_and_equal): fresh(X, X, Y, Z) = Y.
% 0.20/0.39 Axiom 4 (divide_and_equal): fresh2(X, X, Y, Z) = Z.
% 0.20/0.39 Axiom 5 (quotient_smaller_than_numerator): divide(divide(X, Y), X) = zero.
% 0.20/0.39 Axiom 6 (divide_and_equal): fresh(divide(X, Y), zero, Y, X) = fresh2(divide(Y, X), zero, Y, X).
% 0.20/0.39 Axiom 7 (quotient_property): divide(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = zero.
% 0.20/0.39
% 0.20/0.39 Goal 1 (prove_x_divide_zero_is_x): divide(a, zero) = a.
% 0.20/0.39 Proof:
% 0.20/0.39 divide(a, zero)
% 0.20/0.39 = { by axiom 4 (divide_and_equal) R->L }
% 0.20/0.39 fresh2(zero, zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 4 (divide_and_equal) R->L }
% 0.20/0.39 fresh2(fresh2(zero, zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 4 (divide_and_equal) R->L }
% 0.20/0.39 fresh2(fresh2(fresh2(zero, zero, divide(divide(a, divide(a, zero)), zero), zero), zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 7 (quotient_property) R->L }
% 0.20/0.39 fresh2(fresh2(fresh2(divide(divide(divide(a, divide(a, zero)), divide(zero, divide(a, zero))), divide(divide(a, zero), divide(a, zero))), zero, divide(divide(a, divide(a, zero)), zero), zero), zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 2 (zero_is_smallest) }
% 0.20/0.39 fresh2(fresh2(fresh2(divide(divide(divide(a, divide(a, zero)), zero), divide(divide(a, zero), divide(a, zero))), zero, divide(divide(a, divide(a, zero)), zero), zero), zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 1 (x_divide_x_is_zero) }
% 0.20/0.39 fresh2(fresh2(fresh2(divide(divide(divide(a, divide(a, zero)), zero), zero), zero, divide(divide(a, divide(a, zero)), zero), zero), zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 6 (divide_and_equal) R->L }
% 0.20/0.39 fresh2(fresh2(fresh(divide(zero, divide(divide(a, divide(a, zero)), zero)), zero, divide(divide(a, divide(a, zero)), zero), zero), zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 2 (zero_is_smallest) }
% 0.20/0.39 fresh2(fresh2(fresh(zero, zero, divide(divide(a, divide(a, zero)), zero), zero), zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 3 (divide_and_equal) }
% 0.20/0.39 fresh2(fresh2(divide(divide(a, divide(a, zero)), zero), zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 6 (divide_and_equal) R->L }
% 0.20/0.39 fresh2(fresh(divide(zero, divide(a, divide(a, zero))), zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 2 (zero_is_smallest) }
% 0.20/0.39 fresh2(fresh(zero, zero, divide(a, divide(a, zero)), zero), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 3 (divide_and_equal) }
% 0.20/0.39 fresh2(divide(a, divide(a, zero)), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 6 (divide_and_equal) R->L }
% 0.20/0.39 fresh(divide(divide(a, zero), a), zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 5 (quotient_smaller_than_numerator) }
% 0.20/0.39 fresh(zero, zero, a, divide(a, zero))
% 0.20/0.39 = { by axiom 3 (divide_and_equal) }
% 0.20/0.39 a
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39
% 0.20/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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