TSTP Solution File: GEO059-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO059-3 : TPTP v8.1.2. Released v1.0.0.
% 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 : Wed Aug 30 23:27:08 EDT 2023
% Result : Unsatisfiable 0.19s 0.50s
% 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
% 0.07/0.12 % Problem : GEO059-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % 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 : n021.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 : Tue Aug 29 23:16:44 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.50
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 Take the following subset of the input axioms:
% 0.19/0.51 fof(d3, axiom, ![X, V, W, U]: (~equidistant(U, V, W, X) | equidistant(V, U, W, X))).
% 0.19/0.51 fof(d4_4, axiom, ![V2, U2, X2, W2]: (~equidistant(U2, V2, W2, X2) | equidistant(X2, W2, U2, V2))).
% 0.19/0.51 fof(d5, axiom, ![Y, Z, V2, U2, X2, W2]: (~equidistant(U2, V2, W2, X2) | (~equidistant(W2, X2, Y, Z) | equidistant(U2, V2, Y, Z)))).
% 0.19/0.51 fof(prove_congruence, negated_conjecture, ~equidistant(v, u, v, reflection(reflection(u, v), v))).
% 0.19/0.51 fof(r2_2, axiom, ![V2, U2]: equidistant(V2, reflection(U2, V2), U2, V2)).
% 0.19/0.51
% 0.19/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.51 fresh(y, y, x1...xn) = u
% 0.19/0.51 C => fresh(s, t, x1...xn) = v
% 0.19/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.51 variables of u and v.
% 0.19/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.51 input problem has no model of domain size 1).
% 0.19/0.51
% 0.19/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.51
% 0.19/0.51 Axiom 1 (d3): fresh18(X, X, Y, Z, W, V) = true.
% 0.19/0.51 Axiom 2 (d4_4): fresh14(X, X, Y, Z, W, V) = true.
% 0.19/0.51 Axiom 3 (d5): fresh11(X, X, Y, Z, W, V) = true.
% 0.19/0.51 Axiom 4 (r2_2): equidistant(X, reflection(Y, X), Y, X) = true.
% 0.19/0.51 Axiom 5 (d5): fresh12(X, X, Y, Z, W, V, U, T) = equidistant(Y, Z, U, T).
% 0.19/0.51 Axiom 6 (d3): fresh18(equidistant(X, Y, Z, W), true, X, Y, Z, W) = equidistant(Y, X, Z, W).
% 0.19/0.51 Axiom 7 (d4_4): fresh14(equidistant(X, Y, Z, W), true, X, Y, Z, W) = equidistant(W, Z, X, Y).
% 0.19/0.51 Axiom 8 (d5): fresh12(equidistant(X, Y, Z, W), true, V, U, X, Y, Z, W) = fresh11(equidistant(V, U, X, Y), true, V, U, Z, W).
% 0.19/0.51
% 0.19/0.51 Goal 1 (prove_congruence): equidistant(v, u, v, reflection(reflection(u, v), v)) = true.
% 0.19/0.51 Proof:
% 0.19/0.51 equidistant(v, u, v, reflection(reflection(u, v), v))
% 0.19/0.51 = { by axiom 7 (d4_4) R->L }
% 0.19/0.51 fresh14(equidistant(v, reflection(reflection(u, v), v), u, v), true, v, reflection(reflection(u, v), v), u, v)
% 0.19/0.51 = { by axiom 5 (d5) R->L }
% 0.19/0.51 fresh14(fresh12(true, true, v, reflection(reflection(u, v), v), reflection(u, v), v, u, v), true, v, reflection(reflection(u, v), v), u, v)
% 0.19/0.51 = { by axiom 1 (d3) R->L }
% 0.19/0.51 fresh14(fresh12(fresh18(true, true, v, reflection(u, v), u, v), true, v, reflection(reflection(u, v), v), reflection(u, v), v, u, v), true, v, reflection(reflection(u, v), v), u, v)
% 0.19/0.51 = { by axiom 4 (r2_2) R->L }
% 0.19/0.51 fresh14(fresh12(fresh18(equidistant(v, reflection(u, v), u, v), true, v, reflection(u, v), u, v), true, v, reflection(reflection(u, v), v), reflection(u, v), v, u, v), true, v, reflection(reflection(u, v), v), u, v)
% 0.19/0.51 = { by axiom 6 (d3) }
% 0.19/0.51 fresh14(fresh12(equidistant(reflection(u, v), v, u, v), true, v, reflection(reflection(u, v), v), reflection(u, v), v, u, v), true, v, reflection(reflection(u, v), v), u, v)
% 0.19/0.51 = { by axiom 8 (d5) }
% 0.19/0.51 fresh14(fresh11(equidistant(v, reflection(reflection(u, v), v), reflection(u, v), v), true, v, reflection(reflection(u, v), v), u, v), true, v, reflection(reflection(u, v), v), u, v)
% 0.19/0.51 = { by axiom 4 (r2_2) }
% 0.19/0.51 fresh14(fresh11(true, true, v, reflection(reflection(u, v), v), u, v), true, v, reflection(reflection(u, v), v), u, v)
% 0.19/0.51 = { by axiom 3 (d5) }
% 0.19/0.51 fresh14(true, true, v, reflection(reflection(u, v), v), u, v)
% 0.19/0.51 = { by axiom 2 (d4_4) }
% 0.19/0.51 true
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51
% 0.19/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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