TSTP Solution File: SYN058-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN058-1 : 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 : n032.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 03:32:56 EDT 2023
% Result : Unsatisfiable 0.14s 0.33s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYN058-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Aug 26 17:24:29 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.14/0.33 Command-line arguments: --no-flatten-goal
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% 0.14/0.33 % SZS status Unsatisfiable
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% 0.14/0.33 % SZS output start Proof
% 0.14/0.33 Take the following subset of the input axioms:
% 0.14/0.33 fof(clause_1, axiom, ![X, Y]: (~big_p(X) | big_q(Y))).
% 0.14/0.33 fof(clause_3, axiom, ~big_q(b) | big_s(c)).
% 0.14/0.33 fof(clause_6, axiom, ![X2, Y2]: (~big_s(Y2) | (~big_f(X2) | big_g(X2)))).
% 0.14/0.33 fof(clause_7, negated_conjecture, big_p(d)).
% 0.14/0.33 fof(clause_8, negated_conjecture, big_f(d)).
% 0.14/0.33 fof(clause_9, negated_conjecture, ~big_g(d)).
% 0.14/0.33
% 0.14/0.33 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.33 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.33 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.33 fresh(y, y, x1...xn) = u
% 0.14/0.33 C => fresh(s, t, x1...xn) = v
% 0.14/0.33 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.33 variables of u and v.
% 0.14/0.33 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.33 input problem has no model of domain size 1).
% 0.14/0.33
% 0.14/0.33 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.33
% 0.14/0.33 Axiom 1 (clause_7): big_p(d) = true.
% 0.14/0.33 Axiom 2 (clause_8): big_f(d) = true.
% 0.14/0.33 Axiom 3 (clause_3): fresh5(X, X) = true.
% 0.14/0.33 Axiom 4 (clause_6): fresh(X, X, Y) = true.
% 0.14/0.33 Axiom 5 (clause_1): fresh6(X, X, Y) = true.
% 0.14/0.33 Axiom 6 (clause_3): fresh5(big_q(b), true) = big_s(c).
% 0.14/0.33 Axiom 7 (clause_1): fresh6(big_p(X), true, Y) = big_q(Y).
% 0.14/0.33 Axiom 8 (clause_6): fresh2(X, X, Y, Z) = big_g(Z).
% 0.14/0.33 Axiom 9 (clause_6): fresh2(big_f(X), true, Y, X) = fresh(big_s(Y), true, X).
% 0.14/0.33
% 0.14/0.33 Goal 1 (clause_9): big_g(d) = true.
% 0.14/0.33 Proof:
% 0.14/0.33 big_g(d)
% 0.14/0.33 = { by axiom 8 (clause_6) R->L }
% 0.14/0.33 fresh2(true, true, c, d)
% 0.14/0.33 = { by axiom 2 (clause_8) R->L }
% 0.14/0.33 fresh2(big_f(d), true, c, d)
% 0.14/0.33 = { by axiom 9 (clause_6) }
% 0.14/0.33 fresh(big_s(c), true, d)
% 0.14/0.33 = { by axiom 6 (clause_3) R->L }
% 0.14/0.33 fresh(fresh5(big_q(b), true), true, d)
% 0.14/0.33 = { by axiom 7 (clause_1) R->L }
% 0.14/0.33 fresh(fresh5(fresh6(big_p(d), true, b), true), true, d)
% 0.14/0.33 = { by axiom 1 (clause_7) }
% 0.14/0.33 fresh(fresh5(fresh6(true, true, b), true), true, d)
% 0.14/0.33 = { by axiom 5 (clause_1) }
% 0.14/0.33 fresh(fresh5(true, true), true, d)
% 0.14/0.33 = { by axiom 3 (clause_3) }
% 0.14/0.33 fresh(true, true, d)
% 0.14/0.33 = { by axiom 4 (clause_6) }
% 0.14/0.33 true
% 0.14/0.33 % SZS output end Proof
% 0.14/0.33
% 0.14/0.33 RESULT: Unsatisfiable (the axioms are contradictory).
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