TSTP Solution File: GEO056-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO056-2 : 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 : n016.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 23:27:07 EDT 2023
% Result : Unsatisfiable 0.19s 0.41s
% 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 : GEO056-2 : 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
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 19:43:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.41 Command-line arguments: --no-flatten-goal
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% 0.19/0.41 % SZS status Unsatisfiable
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% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Take the following subset of the input axioms:
% 0.19/0.41 fof(identity_for_equidistance, axiom, ![X, Y, Z]: (~equidistant(X, Y, Z, Z) | X=Y)).
% 0.19/0.41 fof(prove_v_equals_reflection, negated_conjecture, v!=reflection(u, v)).
% 0.19/0.41 fof(reflection, axiom, ![V, U]: reflection(U, V)=extension(U, V, U, V)).
% 0.19/0.41 fof(segment_construction2, axiom, ![V2, W, X2, Y2]: equidistant(Y2, extension(X2, Y2, W, V2), W, V2)).
% 0.19/0.41 fof(u_equals_v, hypothesis, u=v).
% 0.19/0.41
% 0.19/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.41 fresh(y, y, x1...xn) = u
% 0.19/0.41 C => fresh(s, t, x1...xn) = v
% 0.19/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.41 variables of u and v.
% 0.19/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.41 input problem has no model of domain size 1).
% 0.19/0.41
% 0.19/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.41
% 0.19/0.41 Axiom 1 (u_equals_v): u = v.
% 0.19/0.41 Axiom 2 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 0.19/0.41 Axiom 3 (reflection): reflection(X, Y) = extension(X, Y, X, Y).
% 0.19/0.41 Axiom 4 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 0.19/0.41 Axiom 5 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 0.19/0.41
% 0.19/0.41 Goal 1 (prove_v_equals_reflection): v = reflection(u, v).
% 0.19/0.41 Proof:
% 0.19/0.41 v
% 0.19/0.41 = { by axiom 1 (u_equals_v) R->L }
% 0.19/0.41 u
% 0.19/0.41 = { by axiom 4 (identity_for_equidistance) R->L }
% 0.19/0.41 fresh(equidistant(u, extension(u, u, u, u), u, u), true, u, extension(u, u, u, u))
% 0.19/0.41 = { by axiom 5 (segment_construction2) }
% 0.19/0.41 fresh(true, true, u, extension(u, u, u, u))
% 0.19/0.41 = { by axiom 2 (identity_for_equidistance) }
% 0.19/0.41 extension(u, u, u, u)
% 0.19/0.41 = { by axiom 3 (reflection) R->L }
% 0.19/0.41 reflection(u, u)
% 0.19/0.41 = { by axiom 1 (u_equals_v) }
% 0.19/0.41 reflection(u, v)
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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