TSTP Solution File: ROB016-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ROB016-1 : 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 : n032.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 14:09:10 EDT 2023
% Result : Unsatisfiable 0.14s 0.35s
% 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
% 0.00/0.09 % Problem : ROB016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 06:56:00 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.35 Command-line arguments: --no-flatten-goal
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% 0.14/0.35 % SZS status Unsatisfiable
% 0.14/0.35
% 0.14/0.35 % SZS output start Proof
% 0.14/0.35 Take the following subset of the input axioms:
% 0.14/0.35 fof(condition, hypothesis, negate(add(d, e))=negate(e)).
% 0.14/0.35 fof(k_positive, axiom, positive_integer(k)).
% 0.14/0.35 fof(lemma_3_6, axiom, ![X, Y, Vk]: (negate(add(negate(Y), negate(add(X, negate(Y)))))!=X | (~positive_integer(Vk) | negate(add(Y, multiply(Vk, add(X, negate(add(X, negate(Y)))))))=negate(Y)))).
% 0.14/0.35 fof(prove_result, negated_conjecture, negate(add(e, multiply(k, add(d, negate(add(d, negate(e)))))))!=negate(e)).
% 0.14/0.35 fof(robbins_axiom, axiom, ![X2, Y2]: negate(add(negate(add(X2, Y2)), negate(add(X2, negate(Y2)))))=X2).
% 0.14/0.35
% 0.14/0.35 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.35 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.35 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.35 fresh(y, y, x1...xn) = u
% 0.14/0.35 C => fresh(s, t, x1...xn) = v
% 0.14/0.35 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.35 variables of u and v.
% 0.14/0.35 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.35 input problem has no model of domain size 1).
% 0.14/0.35
% 0.14/0.35 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.35
% 0.14/0.35 Axiom 1 (k_positive): positive_integer(k) = true.
% 0.14/0.35 Axiom 2 (condition): negate(add(d, e)) = negate(e).
% 0.14/0.35 Axiom 3 (lemma_3_6): fresh3(X, X, Y, Z, W) = negate(Y).
% 0.14/0.35 Axiom 4 (robbins_axiom): negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X.
% 0.14/0.35 Axiom 5 (lemma_3_6): fresh4(X, X, Y, Z, W) = negate(add(Y, multiply(W, add(Z, negate(add(Z, negate(Y))))))).
% 0.14/0.35 Axiom 6 (lemma_3_6): fresh4(positive_integer(X), true, Y, Z, X) = fresh3(negate(add(negate(Y), negate(add(Z, negate(Y))))), Z, Y, Z, X).
% 0.14/0.35
% 0.14/0.35 Goal 1 (prove_result): negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))) = negate(e).
% 0.14/0.35 Proof:
% 0.14/0.35 negate(add(e, multiply(k, add(d, negate(add(d, negate(e)))))))
% 0.14/0.35 = { by axiom 5 (lemma_3_6) R->L }
% 0.14/0.35 fresh4(true, true, e, d, k)
% 0.14/0.35 = { by axiom 1 (k_positive) R->L }
% 0.14/0.35 fresh4(positive_integer(k), true, e, d, k)
% 0.14/0.35 = { by axiom 6 (lemma_3_6) }
% 0.14/0.35 fresh3(negate(add(negate(e), negate(add(d, negate(e))))), d, e, d, k)
% 0.14/0.35 = { by axiom 2 (condition) R->L }
% 0.14/0.35 fresh3(negate(add(negate(add(d, e)), negate(add(d, negate(e))))), d, e, d, k)
% 0.14/0.35 = { by axiom 4 (robbins_axiom) }
% 0.14/0.35 fresh3(d, d, e, d, k)
% 0.14/0.35 = { by axiom 3 (lemma_3_6) }
% 0.14/0.35 negate(e)
% 0.14/0.35 % SZS output end Proof
% 0.14/0.35
% 0.14/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
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