TSTP Solution File: SYN296-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN296-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n001.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 03:33:58 EDT 2023
% Result : Unsatisfiable 28.93s 4.17s
% Output : Proof 28.93s
% 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 : SYN296-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 17:30:31 EDT 2023
% 0.12/0.33 % CPUTime :
% 28.93/4.17 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 28.93/4.17
% 28.93/4.17 % SZS status Unsatisfiable
% 28.93/4.17
% 28.93/4.17 % SZS output start Proof
% 28.93/4.17 Take the following subset of the input axioms:
% 28.93/4.17 fof(axiom_11, axiom, n0(e, b)).
% 28.93/4.17 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 28.93/4.17 fof(prove_this, negated_conjecture, ~q1(e, b, e)).
% 28.93/4.17 fof(rule_092, axiom, ![J, C, B, A2]: (q1(J, A2, J) | (~n0(B, A2) | ~p0(C, J)))).
% 28.93/4.17
% 28.93/4.17 Now clausify the problem and encode Horn clauses using encoding 3 of
% 28.93/4.17 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 28.93/4.17 We repeatedly replace C & s=t => u=v by the two clauses:
% 28.93/4.17 fresh(y, y, x1...xn) = u
% 28.93/4.17 C => fresh(s, t, x1...xn) = v
% 28.93/4.17 where fresh is a fresh function symbol and x1..xn are the free
% 28.93/4.17 variables of u and v.
% 28.93/4.17 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 28.93/4.17 input problem has no model of domain size 1).
% 28.93/4.17
% 28.93/4.17 The encoding turns the above axioms into the following unit equations and goals:
% 28.93/4.17
% 28.93/4.17 Axiom 1 (axiom_14): p0(b, X) = true.
% 28.93/4.17 Axiom 2 (axiom_11): n0(e, b) = true.
% 28.93/4.17 Axiom 3 (rule_092): fresh317(X, X, Y, Z) = true.
% 28.93/4.17 Axiom 4 (rule_092): fresh318(X, X, Y, Z, W) = q1(Y, Z, Y).
% 28.93/4.17 Axiom 5 (rule_092): fresh318(p0(X, Y), true, Y, Z, W) = fresh317(n0(W, Z), true, Y, Z).
% 28.93/4.17
% 28.93/4.17 Goal 1 (prove_this): q1(e, b, e) = true.
% 28.93/4.17 Proof:
% 28.93/4.17 q1(e, b, e)
% 28.93/4.17 = { by axiom 4 (rule_092) R->L }
% 28.93/4.17 fresh318(true, true, e, b, e)
% 28.93/4.17 = { by axiom 1 (axiom_14) R->L }
% 28.93/4.17 fresh318(p0(b, e), true, e, b, e)
% 28.93/4.17 = { by axiom 5 (rule_092) }
% 28.93/4.17 fresh317(n0(e, b), true, e, b)
% 28.93/4.17 = { by axiom 2 (axiom_11) }
% 28.93/4.17 fresh317(true, true, e, b)
% 28.93/4.17 = { by axiom 3 (rule_092) }
% 28.93/4.17 true
% 28.93/4.17 % SZS output end Proof
% 28.93/4.17
% 28.93/4.17 RESULT: Unsatisfiable (the axioms are contradictory).
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