TSTP Solution File: LCL007-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL007-1 : 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 : Thu Aug 31 08:17:01 EDT 2023
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% 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 : LCL007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 19:17:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.38
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 Take the following subset of the input axioms:
% 0.21/0.39 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.21/0.39 fof(ec_4, axiom, ![X2, Y2]: is_a_theorem(equivalent(equivalent(X2, Y2), equivalent(Y2, X2)))).
% 0.21/0.39 fof(ec_5, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(equivalent(equivalent(X2, Y2), Z), equivalent(X2, equivalent(Y2, Z))))).
% 0.21/0.39 fof(prove_ec_2, negated_conjecture, ~is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))).
% 0.21/0.39
% 0.21/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.39 fresh(y, y, x1...xn) = u
% 0.21/0.39 C => fresh(s, t, x1...xn) = v
% 0.21/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.39 variables of u and v.
% 0.21/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.39 input problem has no model of domain size 1).
% 0.21/0.39
% 0.21/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.39
% 0.21/0.39 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.21/0.39 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.21/0.39 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.21/0.39 Axiom 4 (ec_4): is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X))) = true.
% 0.21/0.39 Axiom 5 (ec_5): is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))) = true.
% 0.21/0.39
% 0.21/0.39 Goal 1 (prove_ec_2): is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))) = true.
% 0.21/0.39 Proof:
% 0.21/0.39 is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))
% 0.21/0.39 = { by axiom 2 (condensed_detachment) R->L }
% 0.21/0.39 fresh(true, true, equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))
% 0.21/0.39 = { by axiom 4 (ec_4) R->L }
% 0.21/0.39 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))
% 0.21/0.39 = { by axiom 3 (condensed_detachment) }
% 0.21/0.39 fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true, equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))
% 0.21/0.39 = { by axiom 5 (ec_5) }
% 0.21/0.39 fresh2(true, true, equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))
% 0.21/0.39 = { by axiom 1 (condensed_detachment) }
% 0.21/0.39 true
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39
% 0.21/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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