TSTP Solution File: ROB011-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ROB011-1 : 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 : n022.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 14:09:08 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 : ROB011-1 : 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
% 0.17/0.35 % Computer : n022.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 06:59:09 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.39
% 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(associativity_of_add, axiom, ![X, Y, Z]: add(add(X, Y), Z)=add(X, add(Y, Z))).
% 0.20/0.40 fof(commutativity_of_add, axiom, ![X2, Y2]: add(X2, Y2)=add(Y2, X2)).
% 0.20/0.40 fof(condition, hypothesis, negate(add(a, negate(b)))=c).
% 0.20/0.40 fof(one_times_x, axiom, ![X2]: multiply(one, X2)=X2).
% 0.20/0.40 fof(prove_base_step, negated_conjecture, negate(add(a, negate(add(b, multiply(one, add(a, c))))))!=c).
% 0.20/0.40 fof(robbins_axiom, axiom, ![X2, Y2]: negate(add(negate(add(X2, Y2)), negate(add(X2, negate(Y2)))))=X2).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (one_times_x): multiply(one, X) = X.
% 0.20/0.40 Axiom 2 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.20/0.40 Axiom 3 (condition): negate(add(a, negate(b))) = c.
% 0.20/0.40 Axiom 4 (associativity_of_add): add(add(X, Y), Z) = add(X, add(Y, Z)).
% 0.20/0.40 Axiom 5 (robbins_axiom): negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X.
% 0.20/0.40
% 0.20/0.40 Goal 1 (prove_base_step): negate(add(a, negate(add(b, multiply(one, add(a, c)))))) = c.
% 0.20/0.40 Proof:
% 0.20/0.40 negate(add(a, negate(add(b, multiply(one, add(a, c))))))
% 0.20/0.40 = { by axiom 1 (one_times_x) }
% 0.20/0.40 negate(add(a, negate(add(b, add(a, c)))))
% 0.20/0.40 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.40 negate(add(a, negate(add(b, add(c, a)))))
% 0.20/0.40 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.40 negate(add(a, negate(add(add(c, a), b))))
% 0.20/0.40 = { by axiom 4 (associativity_of_add) }
% 0.20/0.40 negate(add(a, negate(add(c, add(a, b)))))
% 0.20/0.40 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.40 negate(add(a, negate(add(c, add(b, a)))))
% 0.20/0.40 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.40 negate(add(negate(add(c, add(b, a))), a))
% 0.20/0.40 = { by axiom 5 (robbins_axiom) R->L }
% 0.20/0.40 negate(add(negate(add(c, add(b, a))), negate(add(negate(add(a, b)), negate(add(a, negate(b)))))))
% 0.20/0.40 = { by axiom 3 (condition) }
% 0.20/0.40 negate(add(negate(add(c, add(b, a))), negate(add(negate(add(a, b)), c))))
% 0.20/0.40 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.40 negate(add(negate(add(c, add(b, a))), negate(add(c, negate(add(a, b))))))
% 0.20/0.40 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.40 negate(add(negate(add(c, add(b, a))), negate(add(c, negate(add(b, a))))))
% 0.20/0.40 = { by axiom 5 (robbins_axiom) }
% 0.20/0.40 c
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40
% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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