TSTP Solution File: FLD025-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD025-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n008.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 22:36:53 EDT 2023
% Result : Unsatisfiable 57.32s 7.86s
% Output : Proof 58.07s
% 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 : FLD025-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 00:45:32 EDT 2023
% 0.12/0.34 % CPUTime :
% 57.32/7.86 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 57.32/7.86
% 57.32/7.86 % SZS status Unsatisfiable
% 57.32/7.86
% 58.07/7.87 % SZS output start Proof
% 58.07/7.87 Take the following subset of the input axioms:
% 58.07/7.87 fof(a_equals_b_7, negated_conjecture, equalish(a, b)).
% 58.07/7.87 fof(b_is_defined, hypothesis, defined(b)).
% 58.07/7.87 fof(c_equals_d_8, negated_conjecture, equalish(c, d)).
% 58.07/7.87 fof(c_is_defined, hypothesis, defined(c)).
% 58.07/7.87 fof(commutativity_multiplication, axiom, ![X, Y]: (equalish(multiply(X, Y), multiply(Y, X)) | (~defined(X) | ~defined(Y)))).
% 58.07/7.87 fof(compatibility_of_equality_and_multiplication, axiom, ![Z, X2, Y2]: (equalish(multiply(X2, Z), multiply(Y2, Z)) | (~defined(Z) | ~equalish(X2, Y2)))).
% 58.07/7.87 fof(multiply_equals_u_9, negated_conjecture, equalish(multiply(a, c), u)).
% 58.07/7.87 fof(multiply_equals_v_10, negated_conjecture, equalish(multiply(d, b), v)).
% 58.07/7.87 fof(symmetry_of_equality, axiom, ![X2, Y2]: (equalish(X2, Y2) | ~equalish(Y2, X2))).
% 58.07/7.87 fof(transitivity_of_equality, axiom, ![X2, Y2, Z2]: (equalish(X2, Z2) | (~equalish(X2, Y2) | ~equalish(Y2, Z2)))).
% 58.07/7.87 fof(v_not_equal_to_u_11, negated_conjecture, ~equalish(v, u)).
% 58.07/7.87
% 58.07/7.87 Now clausify the problem and encode Horn clauses using encoding 3 of
% 58.07/7.87 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 58.07/7.87 We repeatedly replace C & s=t => u=v by the two clauses:
% 58.07/7.87 fresh(y, y, x1...xn) = u
% 58.07/7.87 C => fresh(s, t, x1...xn) = v
% 58.07/7.87 where fresh is a fresh function symbol and x1..xn are the free
% 58.07/7.87 variables of u and v.
% 58.07/7.87 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 58.07/7.87 input problem has no model of domain size 1).
% 58.07/7.87
% 58.07/7.87 The encoding turns the above axioms into the following unit equations and goals:
% 58.07/7.87
% 58.07/7.87 Axiom 1 (b_is_defined): defined(b) = true.
% 58.07/7.87 Axiom 2 (c_is_defined): defined(c) = true.
% 58.07/7.87 Axiom 3 (a_equals_b_7): equalish(a, b) = true.
% 58.07/7.87 Axiom 4 (c_equals_d_8): equalish(c, d) = true.
% 58.07/7.87 Axiom 5 (multiply_equals_u_9): equalish(multiply(a, c), u) = true.
% 58.07/7.87 Axiom 6 (multiply_equals_v_10): equalish(multiply(d, b), v) = true.
% 58.07/7.87 Axiom 7 (commutativity_multiplication): fresh31(X, X, Y, Z) = true.
% 58.07/7.87 Axiom 8 (symmetry_of_equality): fresh10(X, X, Y, Z) = true.
% 58.07/7.87 Axiom 9 (transitivity_of_equality): fresh8(X, X, Y, Z) = true.
% 58.07/7.87 Axiom 10 (commutativity_multiplication): fresh30(X, X, Y, Z) = fresh31(defined(Y), true, Y, Z).
% 58.07/7.87 Axiom 11 (commutativity_multiplication): fresh30(defined(X), true, Y, X) = equalish(multiply(Y, X), multiply(X, Y)).
% 58.07/7.87 Axiom 12 (compatibility_of_equality_and_multiplication): fresh22(X, X, Y, Z, W) = equalish(multiply(Y, Z), multiply(W, Z)).
% 58.07/7.87 Axiom 13 (compatibility_of_equality_and_multiplication): fresh21(X, X, Y, Z, W) = true.
% 58.07/7.87 Axiom 14 (symmetry_of_equality): fresh10(equalish(X, Y), true, Y, X) = equalish(Y, X).
% 58.07/7.87 Axiom 15 (transitivity_of_equality): fresh9(X, X, Y, Z, W) = equalish(Y, Z).
% 58.07/7.87 Axiom 16 (compatibility_of_equality_and_multiplication): fresh22(defined(X), true, Y, X, Z) = fresh21(equalish(Y, Z), true, Y, X, Z).
% 58.07/7.87 Axiom 17 (transitivity_of_equality): fresh9(equalish(X, Y), true, Z, Y, X) = fresh8(equalish(Z, X), true, Z, Y).
% 58.07/7.87
% 58.07/7.87 Goal 1 (v_not_equal_to_u_11): equalish(v, u) = true.
% 58.07/7.87 Proof:
% 58.07/7.87 equalish(v, u)
% 58.07/7.87 = { by axiom 15 (transitivity_of_equality) R->L }
% 58.07/7.87 fresh9(true, true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 9 (transitivity_of_equality) R->L }
% 58.07/7.87 fresh9(fresh8(true, true, multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 8 (symmetry_of_equality) R->L }
% 58.07/7.87 fresh9(fresh8(fresh10(true, true, multiply(b, c), multiply(a, c)), true, multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 13 (compatibility_of_equality_and_multiplication) R->L }
% 58.07/7.87 fresh9(fresh8(fresh10(fresh21(true, true, a, c, b), true, multiply(b, c), multiply(a, c)), true, multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 3 (a_equals_b_7) R->L }
% 58.07/7.87 fresh9(fresh8(fresh10(fresh21(equalish(a, b), true, a, c, b), true, multiply(b, c), multiply(a, c)), true, multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 16 (compatibility_of_equality_and_multiplication) R->L }
% 58.07/7.87 fresh9(fresh8(fresh10(fresh22(defined(c), true, a, c, b), true, multiply(b, c), multiply(a, c)), true, multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 2 (c_is_defined) }
% 58.07/7.87 fresh9(fresh8(fresh10(fresh22(true, true, a, c, b), true, multiply(b, c), multiply(a, c)), true, multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 12 (compatibility_of_equality_and_multiplication) }
% 58.07/7.87 fresh9(fresh8(fresh10(equalish(multiply(a, c), multiply(b, c)), true, multiply(b, c), multiply(a, c)), true, multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 14 (symmetry_of_equality) }
% 58.07/7.87 fresh9(fresh8(equalish(multiply(b, c), multiply(a, c)), true, multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 17 (transitivity_of_equality) R->L }
% 58.07/7.87 fresh9(fresh9(equalish(multiply(a, c), u), true, multiply(b, c), u, multiply(a, c)), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 5 (multiply_equals_u_9) }
% 58.07/7.87 fresh9(fresh9(true, true, multiply(b, c), u, multiply(a, c)), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 15 (transitivity_of_equality) }
% 58.07/7.87 fresh9(equalish(multiply(b, c), u), true, v, u, multiply(b, c))
% 58.07/7.87 = { by axiom 17 (transitivity_of_equality) }
% 58.07/7.87 fresh8(equalish(v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 14 (symmetry_of_equality) R->L }
% 58.07/7.87 fresh8(fresh10(equalish(multiply(b, c), v), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 15 (transitivity_of_equality) R->L }
% 58.07/7.87 fresh8(fresh10(fresh9(true, true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 9 (transitivity_of_equality) R->L }
% 58.07/7.87 fresh8(fresh10(fresh9(fresh8(true, true, multiply(c, b), v), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 13 (compatibility_of_equality_and_multiplication) R->L }
% 58.07/7.87 fresh8(fresh10(fresh9(fresh8(fresh21(true, true, c, b, d), true, multiply(c, b), v), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 4 (c_equals_d_8) R->L }
% 58.07/7.87 fresh8(fresh10(fresh9(fresh8(fresh21(equalish(c, d), true, c, b, d), true, multiply(c, b), v), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 16 (compatibility_of_equality_and_multiplication) R->L }
% 58.07/7.87 fresh8(fresh10(fresh9(fresh8(fresh22(defined(b), true, c, b, d), true, multiply(c, b), v), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 1 (b_is_defined) }
% 58.07/7.87 fresh8(fresh10(fresh9(fresh8(fresh22(true, true, c, b, d), true, multiply(c, b), v), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 12 (compatibility_of_equality_and_multiplication) }
% 58.07/7.87 fresh8(fresh10(fresh9(fresh8(equalish(multiply(c, b), multiply(d, b)), true, multiply(c, b), v), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 17 (transitivity_of_equality) R->L }
% 58.07/7.87 fresh8(fresh10(fresh9(fresh9(equalish(multiply(d, b), v), true, multiply(c, b), v, multiply(d, b)), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 6 (multiply_equals_v_10) }
% 58.07/7.87 fresh8(fresh10(fresh9(fresh9(true, true, multiply(c, b), v, multiply(d, b)), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 15 (transitivity_of_equality) }
% 58.07/7.87 fresh8(fresh10(fresh9(equalish(multiply(c, b), v), true, multiply(b, c), v, multiply(c, b)), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 17 (transitivity_of_equality) }
% 58.07/7.87 fresh8(fresh10(fresh8(equalish(multiply(b, c), multiply(c, b)), true, multiply(b, c), v), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 11 (commutativity_multiplication) R->L }
% 58.07/7.87 fresh8(fresh10(fresh8(fresh30(defined(c), true, b, c), true, multiply(b, c), v), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 2 (c_is_defined) }
% 58.07/7.87 fresh8(fresh10(fresh8(fresh30(true, true, b, c), true, multiply(b, c), v), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 10 (commutativity_multiplication) }
% 58.07/7.87 fresh8(fresh10(fresh8(fresh31(defined(b), true, b, c), true, multiply(b, c), v), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 1 (b_is_defined) }
% 58.07/7.87 fresh8(fresh10(fresh8(fresh31(true, true, b, c), true, multiply(b, c), v), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 7 (commutativity_multiplication) }
% 58.07/7.87 fresh8(fresh10(fresh8(true, true, multiply(b, c), v), true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 9 (transitivity_of_equality) }
% 58.07/7.87 fresh8(fresh10(true, true, v, multiply(b, c)), true, v, u)
% 58.07/7.87 = { by axiom 8 (symmetry_of_equality) }
% 58.07/7.87 fresh8(true, true, v, u)
% 58.07/7.87 = { by axiom 9 (transitivity_of_equality) }
% 58.07/7.87 true
% 58.07/7.87 % SZS output end Proof
% 58.07/7.87
% 58.07/7.87 RESULT: Unsatisfiable (the axioms are contradictory).
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