TSTP Solution File: GRP096-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP096-1 : 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 : n021.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 01:16:58 EDT 2023
% Result : Unsatisfiable 0.16s 0.36s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP096-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.10/0.11 % 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 : n021.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 23:17:43 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.36 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.16/0.36
% 0.16/0.36 % SZS status Unsatisfiable
% 0.16/0.36
% 0.16/0.37 % SZS output start Proof
% 0.16/0.37 Take the following subset of the input axioms:
% 0.16/0.37 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=divide(X, inverse(Y))).
% 0.16/0.37 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)))).
% 0.16/0.37 fof(single_axiom, axiom, ![Z, X2, Y2]: divide(divide(X2, inverse(divide(Y2, divide(X2, Z)))), Z)=Y2).
% 0.16/0.37
% 0.16/0.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.37 fresh(y, y, x1...xn) = u
% 0.16/0.37 C => fresh(s, t, x1...xn) = v
% 0.16/0.37 where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.37 variables of u and v.
% 0.16/0.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.37 input problem has no model of domain size 1).
% 0.16/0.37
% 0.16/0.37 The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.37
% 0.16/0.37 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.16/0.37 Axiom 2 (single_axiom): divide(divide(X, inverse(divide(Y, divide(X, Z)))), Z) = Y.
% 0.16/0.37
% 0.16/0.37 Lemma 3: divide(multiply(X, divide(Y, divide(X, Z))), Z) = Y.
% 0.16/0.37 Proof:
% 0.16/0.37 divide(multiply(X, divide(Y, divide(X, Z))), Z)
% 0.16/0.37 = { by axiom 1 (multiply) }
% 0.16/0.37 divide(divide(X, inverse(divide(Y, divide(X, Z)))), Z)
% 0.16/0.37 = { by axiom 2 (single_axiom) }
% 0.16/0.38 Y
% 0.16/0.38
% 0.16/0.38 Lemma 4: multiply(multiply(X, divide(Y, multiply(X, Z))), Z) = Y.
% 0.16/0.38 Proof:
% 0.16/0.38 multiply(multiply(X, divide(Y, multiply(X, Z))), Z)
% 0.16/0.38 = { by axiom 1 (multiply) }
% 0.16/0.38 multiply(multiply(X, divide(Y, divide(X, inverse(Z)))), Z)
% 0.16/0.38 = { by axiom 1 (multiply) }
% 0.16/0.38 divide(multiply(X, divide(Y, divide(X, inverse(Z)))), inverse(Z))
% 0.16/0.38 = { by lemma 3 }
% 0.16/0.38 Y
% 0.16/0.38
% 0.16/0.38 Lemma 5: multiply(X, divide(Y, divide(X, multiply(Z, W)))) = multiply(multiply(Z, Y), W).
% 0.16/0.38 Proof:
% 0.16/0.38 multiply(X, divide(Y, divide(X, multiply(Z, W))))
% 0.16/0.38 = { by lemma 4 R->L }
% 0.16/0.38 multiply(multiply(Z, divide(multiply(X, divide(Y, divide(X, multiply(Z, W)))), multiply(Z, W))), W)
% 0.16/0.38 = { by lemma 3 }
% 0.16/0.38 multiply(multiply(Z, Y), W)
% 0.16/0.38
% 0.16/0.38 Lemma 6: divide(multiply(X, Y), X) = Y.
% 0.16/0.38 Proof:
% 0.16/0.38 divide(multiply(X, Y), X)
% 0.16/0.38 = { by lemma 4 R->L }
% 0.16/0.38 divide(multiply(X, Y), multiply(multiply(Z, divide(X, multiply(Z, Y))), Y))
% 0.16/0.38 = { by lemma 4 R->L }
% 0.16/0.38 divide(multiply(multiply(multiply(Z, divide(X, multiply(Z, Y))), Y), Y), multiply(multiply(Z, divide(X, multiply(Z, Y))), Y))
% 0.16/0.38 = { by lemma 5 R->L }
% 0.16/0.38 divide(multiply(W, divide(Y, divide(W, multiply(multiply(Z, divide(X, multiply(Z, Y))), Y)))), multiply(multiply(Z, divide(X, multiply(Z, Y))), Y))
% 0.16/0.38 = { by lemma 3 }
% 0.16/0.38 Y
% 0.16/0.38
% 0.16/0.38 Lemma 7: multiply(multiply(X, Z), Y) = multiply(multiply(X, Y), Z).
% 0.16/0.38 Proof:
% 0.16/0.38 multiply(multiply(X, Z), Y)
% 0.16/0.38 = { by lemma 6 R->L }
% 0.16/0.38 multiply(multiply(X, divide(multiply(multiply(X, Y), Z), multiply(X, Y))), Y)
% 0.16/0.38 = { by lemma 4 }
% 0.16/0.38 multiply(multiply(X, Y), Z)
% 0.16/0.38
% 0.16/0.38 Lemma 8: multiply(multiply(inverse(X), Y), X) = Y.
% 0.16/0.38 Proof:
% 0.16/0.38 multiply(multiply(inverse(X), Y), X)
% 0.16/0.38 = { by axiom 1 (multiply) }
% 0.16/0.38 divide(multiply(inverse(X), Y), inverse(X))
% 0.16/0.38 = { by lemma 6 }
% 0.16/0.38 Y
% 0.16/0.38
% 0.16/0.38 Lemma 9: multiply(multiply(inverse(X), X), Y) = Y.
% 0.16/0.38 Proof:
% 0.16/0.38 multiply(multiply(inverse(X), X), Y)
% 0.16/0.38 = { by lemma 7 }
% 0.16/0.38 multiply(multiply(inverse(X), Y), X)
% 0.16/0.38 = { by lemma 8 }
% 0.16/0.38 Y
% 0.16/0.38
% 0.16/0.38 Lemma 10: multiply(Y, X) = multiply(X, Y).
% 0.16/0.38 Proof:
% 0.16/0.38 multiply(Y, X)
% 0.16/0.38 = { by lemma 9 R->L }
% 0.16/0.38 multiply(multiply(multiply(inverse(Z), Z), Y), X)
% 0.16/0.38 = { by lemma 7 R->L }
% 0.16/0.38 multiply(multiply(multiply(inverse(Z), Z), X), Y)
% 0.16/0.38 = { by lemma 9 }
% 0.16/0.38 multiply(X, Y)
% 0.16/0.38
% 0.16/0.38 Lemma 11: multiply(Z, multiply(Y, X)) = multiply(X, multiply(Y, Z)).
% 0.16/0.38 Proof:
% 0.16/0.38 multiply(Z, multiply(Y, X))
% 0.16/0.38 = { by lemma 10 }
% 0.16/0.38 multiply(multiply(Y, X), Z)
% 0.16/0.38 = { by lemma 5 R->L }
% 0.16/0.38 multiply(W, divide(X, divide(W, multiply(Y, Z))))
% 0.16/0.38 = { by lemma 10 }
% 0.16/0.38 multiply(W, divide(X, divide(W, multiply(Z, Y))))
% 0.16/0.38 = { by lemma 5 }
% 0.16/0.38 multiply(multiply(Z, X), Y)
% 0.16/0.38 = { by lemma 7 R->L }
% 0.16/0.38 multiply(multiply(Z, Y), X)
% 0.16/0.38 = { by lemma 10 R->L }
% 0.16/0.38 multiply(X, multiply(Z, Y))
% 0.16/0.38 = { by lemma 10 R->L }
% 0.16/0.38 multiply(X, multiply(Y, Z))
% 0.16/0.38
% 0.16/0.38 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4)).
% 0.16/0.38 Proof:
% 0.16/0.38 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.38 = { by lemma 9 }
% 0.16/0.38 tuple(multiply(inverse(a1), a1), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.38 = { by lemma 10 R->L }
% 0.16/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.38 = { by lemma 10 R->L }
% 0.16/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 11 R->L }
% 0.16/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(b3, multiply(a3, c3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 10 }
% 0.16/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(b3, multiply(c3, a3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 11 R->L }
% 0.16/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(a3, multiply(c3, b3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 10 R->L }
% 0.16/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 9 R->L }
% 0.16/0.38 tuple(multiply(a1, multiply(multiply(inverse(b1), b1), inverse(a1))), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 10 }
% 0.16/0.38 tuple(multiply(a1, multiply(inverse(a1), multiply(inverse(b1), b1))), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 10 }
% 0.16/0.38 tuple(multiply(multiply(inverse(a1), multiply(inverse(b1), b1)), a1), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 8 }
% 0.16/0.38 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 10 R->L }
% 0.16/0.38 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.16/0.38 = { by lemma 10 }
% 0.16/0.38 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.16/0.38 = { by lemma 10 }
% 0.16/0.38 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.16/0.38 % SZS output end Proof
% 0.16/0.38
% 0.16/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------