TSTP Solution File: SYN066-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN066-1 : 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 : Fri Sep 1 03:33:00 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% 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
% 0.00/0.13 % Problem : SYN066-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 19:47:42 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.39 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.21/0.39 % SZS status Unsatisfiable
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% 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(clause_1, axiom, ![Y, X]: (~big_p(Y, X) | big_p(f(X, Y), g(X)))).
% 0.21/0.39 fof(clause_2, axiom, ![Y2, X2]: big_p(f(X2, Y2), X2)).
% 0.21/0.39 fof(clause_3, axiom, ![Y2, X2]: (~big_p(f(X2, Y2), g(X2)) | big_q(h(X2, Y2), g(X2)))).
% 0.21/0.39 fof(clause_5, axiom, ![Z, Y2, X2]: (~big_q(X2, Y2) | big_r(Z, Z))).
% 0.21/0.39 fof(clause_6, negated_conjecture, ![Z2]: ~big_r(a, Z2)).
% 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 (clause_5): fresh(X, X, Y) = true2.
% 0.21/0.39 Axiom 2 (clause_3): fresh3(X, X, Y, Z) = true2.
% 0.21/0.39 Axiom 3 (clause_1): fresh2(X, X, Y, Z) = true2.
% 0.21/0.39 Axiom 4 (clause_2): big_p(f(X, Y), X) = true2.
% 0.21/0.39 Axiom 5 (clause_5): fresh(big_q(X, Y), true2, Z) = big_r(Z, Z).
% 0.21/0.39 Axiom 6 (clause_1): fresh2(big_p(X, Y), true2, X, Y) = big_p(f(Y, X), g(Y)).
% 0.21/0.39 Axiom 7 (clause_3): fresh3(big_p(f(X, Y), g(X)), true2, X, Y) = big_q(h(X, Y), g(X)).
% 0.21/0.39
% 0.21/0.39 Goal 1 (clause_6): big_r(a, X) = true2.
% 0.21/0.39 The goal is true when:
% 0.21/0.39 X = a
% 0.21/0.39
% 0.21/0.39 Proof:
% 0.21/0.39 big_r(a, a)
% 0.21/0.39 = { by axiom 5 (clause_5) R->L }
% 0.21/0.39 fresh(big_q(h(X, f(X, Y)), g(X)), true2, a)
% 0.21/0.39 = { by axiom 7 (clause_3) R->L }
% 0.21/0.39 fresh(fresh3(big_p(f(X, f(X, Y)), g(X)), true2, X, f(X, Y)), true2, a)
% 0.21/0.39 = { by axiom 6 (clause_1) R->L }
% 0.21/0.39 fresh(fresh3(fresh2(big_p(f(X, Y), X), true2, f(X, Y), X), true2, X, f(X, Y)), true2, a)
% 0.21/0.39 = { by axiom 4 (clause_2) }
% 0.21/0.39 fresh(fresh3(fresh2(true2, true2, f(X, Y), X), true2, X, f(X, Y)), true2, a)
% 0.21/0.39 = { by axiom 3 (clause_1) }
% 0.21/0.39 fresh(fresh3(true2, true2, X, f(X, Y)), true2, a)
% 0.21/0.39 = { by axiom 2 (clause_3) }
% 0.21/0.39 fresh(true2, true2, a)
% 0.21/0.39 = { by axiom 1 (clause_5) }
% 0.21/0.39 true2
% 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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