TSTP Solution File: GRP087-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP087-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n001.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 01:16:56 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% 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 : GRP087-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n001.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 : Mon Aug 28 21:00:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
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% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Take the following subset of the input axioms:
% 0.20/0.42 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1) | (multiply(multiply(inverse(b2), b2), a2)!=a2 | (multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)) | multiply(a4, b4)!=multiply(b4, a4)))).
% 0.20/0.42 fof(single_axiom, axiom, ![X, Y, Z]: multiply(X, multiply(multiply(inverse(multiply(X, Y)), Z), Y))=Z).
% 0.20/0.42
% 0.20/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.42 fresh(y, y, x1...xn) = u
% 0.20/0.42 C => fresh(s, t, x1...xn) = v
% 0.20/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.42 variables of u and v.
% 0.20/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.42 input problem has no model of domain size 1).
% 0.20/0.42
% 0.20/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.42
% 0.20/0.42 Axiom 1 (single_axiom): multiply(X, multiply(multiply(inverse(multiply(X, Y)), Z), Y)) = Z.
% 0.20/0.42
% 0.20/0.42 Lemma 2: multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z) = multiply(X, multiply(W, Y)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z)
% 0.20/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.42 multiply(X, multiply(multiply(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z)), Y))
% 0.20/0.42 = { by axiom 1 (single_axiom) }
% 0.20/0.42 multiply(X, multiply(W, Y))
% 0.20/0.42
% 0.20/0.42 Lemma 3: multiply(multiply(inverse(X), Y), multiply(Z, multiply(X, W))) = multiply(Z, multiply(Y, W)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(multiply(inverse(X), Y), multiply(Z, multiply(X, W)))
% 0.20/0.42 = { by lemma 2 R->L }
% 0.20/0.42 multiply(multiply(inverse(X), Y), multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), X), V))
% 0.20/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.42 multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), X), V))), Y), multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), X), V))
% 0.20/0.42 = { by lemma 2 }
% 0.20/0.42 multiply(Z, multiply(Y, W))
% 0.20/0.42
% 0.20/0.42 Lemma 4: multiply(multiply(inverse(X), Y), multiply(Z, multiply(X, W))) = multiply(multiply(inverse(V), Z), multiply(V, multiply(Y, W))).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(multiply(inverse(X), Y), multiply(Z, multiply(X, W)))
% 0.20/0.42 = { by lemma 3 R->L }
% 0.20/0.42 multiply(multiply(inverse(V), Z), multiply(multiply(inverse(X), Y), multiply(V, multiply(X, W))))
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 multiply(multiply(inverse(V), Z), multiply(V, multiply(Y, W)))
% 0.20/0.42
% 0.20/0.42 Lemma 5: multiply(X, multiply(Y, Z)) = multiply(Y, multiply(X, Z)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(Y, Z))
% 0.20/0.42 = { by lemma 3 R->L }
% 0.20/0.42 multiply(multiply(inverse(W), Y), multiply(X, multiply(W, Z)))
% 0.20/0.42 = { by lemma 4 }
% 0.20/0.42 multiply(multiply(inverse(Y), X), multiply(Y, multiply(Y, Z)))
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 multiply(Y, multiply(X, Z))
% 0.20/0.42
% 0.20/0.42 Lemma 6: multiply(X, multiply(multiply(inverse(X), Y), Z)) = multiply(Y, Z).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(multiply(inverse(X), Y), Z))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 multiply(multiply(inverse(X), Y), multiply(X, Z))
% 0.20/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.42 multiply(multiply(inverse(X), Y), multiply(X, multiply(W, multiply(multiply(inverse(multiply(W, V)), Z), V))))
% 0.20/0.42 = { by lemma 4 R->L }
% 0.20/0.42 multiply(multiply(inverse(U), W), multiply(Y, multiply(U, multiply(multiply(inverse(multiply(W, V)), Z), V))))
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 multiply(Y, multiply(W, multiply(multiply(inverse(multiply(W, V)), Z), V)))
% 0.20/0.42 = { by axiom 1 (single_axiom) }
% 0.20/0.42 multiply(Y, Z)
% 0.20/0.42
% 0.20/0.42 Lemma 7: multiply(inverse(multiply(X, Y)), multiply(X, multiply(Z, Y))) = Z.
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(inverse(multiply(X, Y)), multiply(X, multiply(Z, Y)))
% 0.20/0.42 = { by lemma 2 R->L }
% 0.20/0.42 multiply(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z), W))
% 0.20/0.42 = { by axiom 1 (single_axiom) }
% 0.20/0.42 Z
% 0.20/0.42
% 0.20/0.42 Lemma 8: multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(multiply(X, Y), Z)
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 multiply(W, multiply(multiply(inverse(W), multiply(X, Y)), Z))
% 0.20/0.42 = { by lemma 3 R->L }
% 0.20/0.42 multiply(multiply(inverse(multiply(inverse(W), Y)), multiply(inverse(W), multiply(X, Y))), multiply(W, multiply(multiply(inverse(W), Y), Z)))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 multiply(X, multiply(W, multiply(multiply(inverse(W), Y), Z)))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 multiply(X, multiply(Y, Z))
% 0.20/0.42
% 0.20/0.42 Lemma 9: multiply(X, multiply(inverse(X), multiply(Y, Z))) = multiply(Y, Z).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(inverse(X), multiply(Y, Z)))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 multiply(inverse(X), multiply(X, multiply(Y, Z)))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 multiply(inverse(X), multiply(Y, multiply(X, Z)))
% 0.20/0.42 = { by lemma 8 R->L }
% 0.20/0.42 multiply(multiply(inverse(X), Y), multiply(X, Z))
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.42 multiply(multiply(inverse(X), Y), multiply(X, multiply(inverse(multiply(W, V)), multiply(W, multiply(Z, V)))))
% 0.20/0.42 = { by lemma 4 R->L }
% 0.20/0.42 multiply(multiply(inverse(U), inverse(multiply(W, V))), multiply(Y, multiply(U, multiply(W, multiply(Z, V)))))
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 multiply(Y, multiply(inverse(multiply(W, V)), multiply(W, multiply(Z, V))))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 multiply(Y, Z)
% 0.20/0.42
% 0.20/0.42 Lemma 10: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(inverse(X), Y))
% 0.20/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.42 multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(multiply(Z, W)), Y), W))))
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 multiply(Z, multiply(multiply(inverse(multiply(Z, W)), Y), W))
% 0.20/0.42 = { by axiom 1 (single_axiom) }
% 0.20/0.42 Y
% 0.20/0.42
% 0.20/0.42 Lemma 11: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(inverse(X), X)
% 0.20/0.43 = { by lemma 9 R->L }
% 0.20/0.43 multiply(Y, multiply(inverse(Y), multiply(inverse(X), X)))
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 multiply(Y, multiply(inverse(X), multiply(inverse(Y), X)))
% 0.20/0.43 = { by lemma 10 R->L }
% 0.20/0.43 multiply(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), X))), multiply(inverse(Y), X)))
% 0.20/0.43 = { by lemma 10 R->L }
% 0.20/0.43 multiply(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), X))), multiply(Y, multiply(inverse(Y), multiply(inverse(Y), X)))))
% 0.20/0.43 = { by lemma 7 }
% 0.20/0.43 multiply(Y, inverse(Y))
% 0.20/0.43
% 0.20/0.43 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4)).
% 0.20/0.43 Proof:
% 0.20/0.43 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.20/0.43 = { by lemma 8 }
% 0.20/0.43 tuple(multiply(inverse(b2), multiply(b2, a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.20/0.43 = { by lemma 8 }
% 0.20/0.43 tuple(multiply(inverse(b2), multiply(b2, a2)), multiply(a3, multiply(b3, c3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 tuple(multiply(b2, multiply(inverse(b2), a2)), multiply(a3, multiply(b3, c3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.20/0.43 = { by lemma 11 }
% 0.20/0.43 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(a4, b4))
% 0.20/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.43 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(Y, multiply(multiply(inverse(multiply(Y, Z)), multiply(a4, b4)), Z)))
% 0.20/0.43 = { by lemma 8 R->L }
% 0.20/0.43 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(Y, multiply(multiply(multiply(inverse(multiply(Y, Z)), a4), b4), Z)))
% 0.20/0.43 = { by lemma 7 R->L }
% 0.20/0.43 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(Y, multiply(multiply(multiply(inverse(multiply(Y, Z)), a4), multiply(inverse(multiply(inverse(multiply(Y, Z)), a4)), multiply(inverse(multiply(Y, Z)), multiply(b4, a4)))), Z)))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(Y, multiply(multiply(inverse(multiply(Y, Z)), multiply(b4, a4)), Z)))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.43 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(b4, a4))
% 0.20/0.43 = { by lemma 11 R->L }
% 0.20/0.43 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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