TSTP Solution File: ALG003-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG003-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 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 : n002.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 : Wed Aug 30 16:41:57 EDT 2023
% Result : Unsatisfiable 3.45s 0.86s
% Output : Proof 3.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ALG003-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 0.11/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 03:13:04 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.45/0.86 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.45/0.86
% 3.45/0.86 % SZS status Unsatisfiable
% 3.45/0.86
% 3.45/0.86 % SZS output start Proof
% 3.45/0.86 Take the following subset of the input axioms:
% 3.45/0.86 fof(idempotent_element, hypothesis, multiply(an_element, an_element)=an_element).
% 3.45/0.86 fof(left_cancellation, axiom, ![X, Y, Z, U]: (multiply(X, Y)!=Z | (multiply(U, Y)!=Z | X=U))).
% 3.45/0.86 fof(medial_law, axiom, ![X2, Y2, Z2, U2]: multiply(multiply(X2, Y2), multiply(Z2, U2))=multiply(multiply(X2, Z2), multiply(Y2, U2))).
% 3.45/0.86 fof(prove_this, negated_conjecture, multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f))!=multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f))).
% 3.45/0.86
% 3.45/0.86 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.45/0.86 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.45/0.86 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.45/0.86 fresh(y, y, x1...xn) = u
% 3.45/0.86 C => fresh(s, t, x1...xn) = v
% 3.45/0.86 where fresh is a fresh function symbol and x1..xn are the free
% 3.45/0.86 variables of u and v.
% 3.45/0.86 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.45/0.86 input problem has no model of domain size 1).
% 3.45/0.86
% 3.45/0.86 The encoding turns the above axioms into the following unit equations and goals:
% 3.45/0.86
% 3.45/0.86 Axiom 1 (idempotent_element): multiply(an_element, an_element) = an_element.
% 3.45/0.86 Axiom 2 (left_cancellation): fresh4(X, X, Y, Z) = Z.
% 3.45/0.86 Axiom 3 (medial_law): multiply(multiply(X, Y), multiply(Z, W)) = multiply(multiply(X, Z), multiply(Y, W)).
% 3.45/0.86 Axiom 4 (left_cancellation): fresh3(X, X, Y, Z, W, V) = Y.
% 3.45/0.86 Axiom 5 (left_cancellation): fresh3(multiply(X, Y), Z, W, Y, Z, X) = fresh4(multiply(W, Y), Z, W, X).
% 3.45/0.86
% 3.45/0.86 Lemma 6: multiply(multiply(X, an_element), multiply(Y, an_element)) = multiply(multiply(X, Y), an_element).
% 3.45/0.86 Proof:
% 3.45/0.86 multiply(multiply(X, an_element), multiply(Y, an_element))
% 3.45/0.86 = { by axiom 3 (medial_law) R->L }
% 3.45/0.86 multiply(multiply(X, Y), multiply(an_element, an_element))
% 3.45/0.86 = { by axiom 1 (idempotent_element) }
% 3.45/0.86 multiply(multiply(X, Y), an_element)
% 3.45/0.86
% 3.45/0.86 Goal 1 (prove_this): multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)) = multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)).
% 3.45/0.86 Proof:
% 3.45/0.86 multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f))
% 3.45/0.86 = { by axiom 4 (left_cancellation) R->L }
% 3.45/0.86 fresh3(multiply(multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)), an_element), multiply(multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)), an_element), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element, multiply(multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)), an_element), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.86 = { by axiom 5 (left_cancellation) }
% 3.45/0.86 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)), an_element), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.86 = { by lemma 6 R->L }
% 3.45/0.86 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(b, c)), an_element), multiply(multiply(multiply(d, e), f), an_element)), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.86 = { by lemma 6 R->L }
% 3.45/0.86 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(b, c)), an_element), multiply(multiply(multiply(d, e), an_element), multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.86 = { by axiom 3 (medial_law) R->L }
% 3.45/0.86 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), an_element)), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.86 = { by axiom 1 (idempotent_element) R->L }
% 3.45/0.86 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), multiply(an_element, an_element))), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.86 = { by axiom 3 (medial_law) }
% 3.45/0.86 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), multiply(an_element, an_element))), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.86 = { by axiom 3 (medial_law) }
% 3.45/0.86 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(d, e)), multiply(multiply(b, an_element), multiply(c, an_element))), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by axiom 3 (medial_law) R->L }
% 3.45/0.87 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(b, an_element)), multiply(multiply(d, e), multiply(c, an_element))), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by axiom 3 (medial_law) R->L }
% 3.45/0.87 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(b, an_element)), multiply(multiply(d, c), multiply(e, an_element))), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by axiom 3 (medial_law) R->L }
% 3.45/0.87 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, an_element), multiply(e, an_element))), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by axiom 3 (medial_law) R->L }
% 3.45/0.87 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), multiply(an_element, an_element))), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by axiom 1 (idempotent_element) }
% 3.45/0.87 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), an_element)), multiply(an_element, multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by axiom 3 (medial_law) }
% 3.45/0.87 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(d, c)), an_element), multiply(multiply(multiply(b, e), an_element), multiply(f, an_element))), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by lemma 6 }
% 3.45/0.87 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(d, c)), an_element), multiply(multiply(multiply(b, e), f), an_element)), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by lemma 6 }
% 3.45/0.87 fresh4(multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), an_element), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))
% 3.45/0.87 = { by axiom 2 (left_cancellation) }
% 3.45/0.87 multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f))
% 3.45/0.87 % SZS output end Proof
% 3.45/0.87
% 3.45/0.87 RESULT: Unsatisfiable (the axioms are contradictory).
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