TSTP Solution File: ALG004-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG004-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n031.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 25.25s 3.79s
% Output : Proof 25.30s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG004-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.31 % Computer : n031.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Aug 28 05:17:24 EDT 2023
% 0.10/0.32 % CPUTime :
% 25.25/3.79 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 25.25/3.79
% 25.25/3.79 % SZS status Unsatisfiable
% 25.25/3.79
% 25.30/3.80 % SZS output start Proof
% 25.30/3.80 Take the following subset of the input axioms:
% 25.30/3.80 fof(left_cancellation, axiom, ![X, Y, Z, U]: (multiply(X, Y)!=Z | (multiply(U, Y)!=Z | X=U))).
% 25.30/3.80 fof(medial_law, axiom, ![X2, Y2, Z2, U2]: multiply(multiply(X2, Y2), multiply(Z2, U2))=multiply(multiply(X2, Z2), multiply(Y2, U2))).
% 25.30/3.80 fof(prove_quotient_condition1, negated_conjecture, multiply(b, b0)=multiply(a, a0)).
% 25.30/3.80 fof(prove_quotient_condition2, negated_conjecture, multiply(d, b0)=multiply(c, a0)).
% 25.30/3.80 fof(prove_quotient_condition3, negated_conjecture, multiply(b, d0)=multiply(a, c0)).
% 25.30/3.80 fof(prove_quotient_condition4, negated_conjecture, multiply(d, d0)!=multiply(c, c0)).
% 25.30/3.80 fof(right_cancelaation, axiom, ![X2, Y2, Z2, U2]: (multiply(X2, Y2)!=Z2 | (multiply(X2, U2)!=Z2 | Y2=U2))).
% 25.30/3.80
% 25.30/3.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 25.30/3.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 25.30/3.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 25.30/3.80 fresh(y, y, x1...xn) = u
% 25.30/3.80 C => fresh(s, t, x1...xn) = v
% 25.30/3.80 where fresh is a fresh function symbol and x1..xn are the free
% 25.30/3.80 variables of u and v.
% 25.30/3.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 25.30/3.80 input problem has no model of domain size 1).
% 25.30/3.80
% 25.30/3.80 The encoding turns the above axioms into the following unit equations and goals:
% 25.30/3.80
% 25.30/3.80 Axiom 1 (prove_quotient_condition2): multiply(d, b0) = multiply(c, a0).
% 25.30/3.80 Axiom 2 (prove_quotient_condition3): multiply(b, d0) = multiply(a, c0).
% 25.30/3.80 Axiom 3 (prove_quotient_condition1): multiply(b, b0) = multiply(a, a0).
% 25.30/3.80 Axiom 4 (right_cancelaation): fresh(X, X, Y, Z) = Z.
% 25.30/3.80 Axiom 5 (left_cancellation): fresh4(X, X, Y, Z) = Z.
% 25.30/3.80 Axiom 6 (medial_law): multiply(multiply(X, Y), multiply(Z, W)) = multiply(multiply(X, Z), multiply(Y, W)).
% 25.30/3.80 Axiom 7 (left_cancellation): fresh3(X, X, Y, Z, W, V) = Y.
% 25.30/3.80 Axiom 8 (right_cancelaation): fresh2(X, X, Y, Z, W, V) = Z.
% 25.30/3.80 Axiom 9 (left_cancellation): fresh3(multiply(X, Y), Z, W, Y, Z, X) = fresh4(multiply(W, Y), Z, W, X).
% 25.30/3.80 Axiom 10 (right_cancelaation): fresh2(multiply(X, Y), Z, X, W, Z, Y) = fresh(multiply(X, W), Z, W, Y).
% 25.30/3.80
% 25.30/3.80 Lemma 11: multiply(multiply(X, multiply(Y, Z)), multiply(W, multiply(V, U))) = multiply(multiply(X, W), multiply(multiply(Y, V), multiply(Z, U))).
% 25.30/3.80 Proof:
% 25.30/3.80 multiply(multiply(X, multiply(Y, Z)), multiply(W, multiply(V, U)))
% 25.30/3.80 = { by axiom 6 (medial_law) R->L }
% 25.30/3.80 multiply(multiply(X, W), multiply(multiply(Y, Z), multiply(V, U)))
% 25.30/3.80 = { by axiom 6 (medial_law) R->L }
% 25.30/3.80 multiply(multiply(X, W), multiply(multiply(Y, V), multiply(Z, U)))
% 25.30/3.80
% 25.30/3.80 Goal 1 (prove_quotient_condition4): multiply(d, d0) = multiply(c, c0).
% 25.30/3.80 Proof:
% 25.30/3.80 multiply(d, d0)
% 25.30/3.80 = { by axiom 7 (left_cancellation) R->L }
% 25.30/3.80 fresh3(multiply(multiply(c, c0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X)), multiply(d, d0), multiply(b0, X), multiply(multiply(c, c0), multiply(b0, X)), multiply(c, c0))
% 25.30/3.80 = { by axiom 9 (left_cancellation) }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X)), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 4 (right_cancelaation) R->L }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 6 (medial_law) }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, d), multiply(b, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 2 (prove_quotient_condition3) }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, d), multiply(a, c0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 6 (medial_law) R->L }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, a), multiply(d, c0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 6 (medial_law) }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, a), multiply(d, d0)), multiply(multiply(d, c0), multiply(b0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 6 (medial_law) R->L }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, a), multiply(d, d0)), multiply(multiply(d, b0), multiply(c0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 1 (prove_quotient_condition2) }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, a), multiply(d, d0)), multiply(multiply(c, a0), multiply(c0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 6 (medial_law) R->L }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, a), multiply(d, d0)), multiply(multiply(c, c0), multiply(a0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by lemma 11 R->L }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, a), multiply(c, a0)), multiply(multiply(d, d0), multiply(c0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 6 (medial_law) R->L }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, c), multiply(a, a0)), multiply(multiply(d, d0), multiply(c0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 3 (prove_quotient_condition1) R->L }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, c), multiply(b, b0)), multiply(multiply(d, d0), multiply(c0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 6 (medial_law) }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, b), multiply(c, b0)), multiply(multiply(d, d0), multiply(c0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by lemma 11 }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X))), multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(c, c0), multiply(b0, X))), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 10 (right_cancelaation) R->L }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), fresh2(multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(c, c0), multiply(b0, X))), multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(c, c0), multiply(b0, X))), multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(multiply(Y, b), multiply(d, d0)), multiply(multiply(c, c0), multiply(b0, X))), multiply(multiply(c, c0), multiply(b0, X))), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 8 (right_cancelaation) }
% 25.30/3.80 fresh4(multiply(multiply(d, d0), multiply(b0, X)), multiply(multiply(d, d0), multiply(b0, X)), multiply(d, d0), multiply(c, c0))
% 25.30/3.80 = { by axiom 5 (left_cancellation) }
% 25.30/3.80 multiply(c, c0)
% 25.30/3.80 % SZS output end Proof
% 25.30/3.80
% 25.30/3.80 RESULT: Unsatisfiable (the axioms are contradictory).
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