TSTP Solution File: SYN068-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN068-1 : 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 : n007.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 03:33:01 EDT 2023
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN068-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.31 % Computer : n007.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat Aug 26 19:12:12 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.12/0.36 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.12/0.36 % SZS status Unsatisfiable
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% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 Take the following subset of the input axioms:
% 0.12/0.36 fof(clause_3, axiom, ![X]: (~big_f(X) | big_g(g(X)))).
% 0.12/0.36 fof(clause_4, axiom, ![X2]: (~big_f(X2) | ~big_h(X2, g(X2)))).
% 0.12/0.36 fof(clause_5, axiom, big_j(a)).
% 0.12/0.36 fof(clause_6, axiom, ![X2]: (~big_g(X2) | big_h(a, X2))).
% 0.12/0.36 fof(clause_7, negated_conjecture, ![X2]: (~big_j(X2) | big_f(X2))).
% 0.12/0.36
% 0.12/0.36 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.12/0.36 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.12/0.36 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.12/0.36 fresh(y, y, x1...xn) = u
% 0.12/0.36 C => fresh(s, t, x1...xn) = v
% 0.12/0.36 where fresh is a fresh function symbol and x1..xn are the free
% 0.12/0.36 variables of u and v.
% 0.12/0.36 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.12/0.36 input problem has no model of domain size 1).
% 0.12/0.36
% 0.12/0.36 The encoding turns the above axioms into the following unit equations and goals:
% 0.12/0.36
% 0.12/0.36 Axiom 1 (clause_5): big_j(a) = true2.
% 0.12/0.36 Axiom 2 (clause_7): fresh(X, X, Y) = true2.
% 0.12/0.36 Axiom 3 (clause_3): fresh3(X, X, Y) = true2.
% 0.12/0.36 Axiom 4 (clause_6): fresh2(X, X, Y) = true2.
% 0.12/0.36 Axiom 5 (clause_7): fresh(big_j(X), true2, X) = big_f(X).
% 0.12/0.36 Axiom 6 (clause_3): fresh3(big_f(X), true2, X) = big_g(g(X)).
% 0.12/0.36 Axiom 7 (clause_6): fresh2(big_g(X), true2, X) = big_h(a, X).
% 0.12/0.36
% 0.12/0.36 Lemma 8: big_f(a) = true2.
% 0.12/0.36 Proof:
% 0.12/0.36 big_f(a)
% 0.12/0.36 = { by axiom 5 (clause_7) R->L }
% 0.12/0.36 fresh(big_j(a), true2, a)
% 0.12/0.36 = { by axiom 1 (clause_5) }
% 0.12/0.36 fresh(true2, true2, a)
% 0.12/0.36 = { by axiom 2 (clause_7) }
% 0.12/0.36 true2
% 0.12/0.36
% 0.12/0.36 Goal 1 (clause_4): tuple(big_f(X), big_h(X, g(X))) = tuple(true2, true2).
% 0.12/0.36 The goal is true when:
% 0.12/0.36 X = a
% 0.12/0.36
% 0.12/0.36 Proof:
% 0.12/0.36 tuple(big_f(a), big_h(a, g(a)))
% 0.12/0.36 = { by axiom 7 (clause_6) R->L }
% 0.12/0.36 tuple(big_f(a), fresh2(big_g(g(a)), true2, g(a)))
% 0.12/0.36 = { by axiom 6 (clause_3) R->L }
% 0.12/0.36 tuple(big_f(a), fresh2(fresh3(big_f(a), true2, a), true2, g(a)))
% 0.12/0.36 = { by lemma 8 }
% 0.12/0.36 tuple(big_f(a), fresh2(fresh3(true2, true2, a), true2, g(a)))
% 0.12/0.36 = { by axiom 3 (clause_3) }
% 0.12/0.36 tuple(big_f(a), fresh2(true2, true2, g(a)))
% 0.12/0.36 = { by axiom 4 (clause_6) }
% 0.12/0.36 tuple(big_f(a), true2)
% 0.12/0.36 = { by lemma 8 }
% 0.12/0.36 tuple(true2, true2)
% 0.12/0.36 % SZS output end Proof
% 0.12/0.36
% 0.12/0.36 RESULT: Unsatisfiable (the axioms are contradictory).
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