TSTP Solution File: FLD030-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : FLD030-1 : 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 : 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 : Wed Aug 30 22:36:55 EDT 2023
% Result : Unsatisfiable 0.19s 0.53s
% Output : Proof 0.19s
% 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 : FLD030-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.13 % 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 01:04:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.53 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.53
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53
% 0.19/0.53 % SZS output start Proof
% 0.19/0.53 Take the following subset of the input axioms:
% 0.19/0.53 fof(a_equals_d_4, negated_conjecture, equalish(a, d)).
% 0.19/0.53 fof(b_is_defined, hypothesis, defined(b)).
% 0.19/0.54 fof(compatibility_of_equality_and_multiplication, axiom, ![X, Y, Z]: (equalish(multiply(X, Z), multiply(Y, Z)) | (~defined(Z) | ~equalish(X, Y)))).
% 0.19/0.54 fof(multiply_not_equal_to_multiply_5, negated_conjecture, ~equalish(multiply(d, b), multiply(a, b))).
% 0.19/0.54 fof(symmetry_of_equality, axiom, ![X2, Y2]: (equalish(X2, Y2) | ~equalish(Y2, X2))).
% 0.19/0.54
% 0.19/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.54 fresh(y, y, x1...xn) = u
% 0.19/0.54 C => fresh(s, t, x1...xn) = v
% 0.19/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.54 variables of u and v.
% 0.19/0.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.54 input problem has no model of domain size 1).
% 0.19/0.54
% 0.19/0.54 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.54
% 0.19/0.54 Axiom 1 (b_is_defined): defined(b) = true.
% 0.19/0.54 Axiom 2 (a_equals_d_4): equalish(a, d) = true.
% 0.19/0.54 Axiom 3 (symmetry_of_equality): fresh10(X, X, Y, Z) = true.
% 0.19/0.54 Axiom 4 (compatibility_of_equality_and_multiplication): fresh21(X, X, Y, Z, W) = true.
% 0.19/0.54 Axiom 5 (symmetry_of_equality): fresh10(equalish(X, Y), true, Y, X) = equalish(Y, X).
% 0.19/0.54 Axiom 6 (compatibility_of_equality_and_multiplication): fresh22(X, X, Y, Z, W) = equalish(multiply(Y, Z), multiply(W, Z)).
% 0.19/0.54 Axiom 7 (compatibility_of_equality_and_multiplication): fresh22(defined(X), true, Y, X, Z) = fresh21(equalish(Y, Z), true, Y, X, Z).
% 0.19/0.54
% 0.19/0.54 Goal 1 (multiply_not_equal_to_multiply_5): equalish(multiply(d, b), multiply(a, b)) = true.
% 0.19/0.54 Proof:
% 0.19/0.54 equalish(multiply(d, b), multiply(a, b))
% 0.19/0.54 = { by axiom 6 (compatibility_of_equality_and_multiplication) R->L }
% 0.19/0.54 fresh22(true, true, d, b, a)
% 0.19/0.54 = { by axiom 1 (b_is_defined) R->L }
% 0.19/0.54 fresh22(defined(b), true, d, b, a)
% 0.19/0.54 = { by axiom 7 (compatibility_of_equality_and_multiplication) }
% 0.19/0.54 fresh21(equalish(d, a), true, d, b, a)
% 0.19/0.54 = { by axiom 5 (symmetry_of_equality) R->L }
% 0.19/0.54 fresh21(fresh10(equalish(a, d), true, d, a), true, d, b, a)
% 0.19/0.54 = { by axiom 2 (a_equals_d_4) }
% 0.19/0.54 fresh21(fresh10(true, true, d, a), true, d, b, a)
% 0.19/0.54 = { by axiom 3 (symmetry_of_equality) }
% 0.19/0.54 fresh21(true, true, d, b, a)
% 0.19/0.54 = { by axiom 4 (compatibility_of_equality_and_multiplication) }
% 0.19/0.54 true
% 0.19/0.54 % SZS output end Proof
% 0.19/0.54
% 0.19/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
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