TSTP Solution File: PUZ038-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ038-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n014.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 13:24:02 EDT 2023
% Result : Unsatisfiable 0.21s 0.55s
% 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 : PUZ038-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n014.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 : Sat Aug 26 22:24:02 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.55 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.55
% 0.21/0.55 % SZS status Unsatisfiable
% 0.21/0.55
% 0.21/0.55 % SZS output start Proof
% 0.21/0.55 Take the following subset of the input axioms:
% 0.21/0.55 fof(goal_state, negated_conjecture, ![B, V1, V2, V4, H, S2, S3, S4, E2, S1, E1]: ~state(B, V1, V2, v3(s(s(s(o))), o), V4, H, S1, S2, S3, S4, E1, E2)).
% 0.21/0.55 fof(initial_state, hypothesis, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), o), e2(s(s(s(s(o)))), s(s(s(o)))))).
% 0.21/0.55 fof(v3_down, axiom, ![X, Y, B2, V1_2, V2_2, V4_2, H2, S2_2, S3_2, S4_2, E2_2, S1_2]: (~state(B2, V1_2, V2_2, v3(X, Y), V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(s(s(X)), Y), E2_2) | state(B2, V1_2, V2_2, v3(s(X), Y), V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(X, Y), E2_2))).
% 0.21/0.55
% 0.21/0.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.55 fresh(y, y, x1...xn) = u
% 0.21/0.55 C => fresh(s, t, x1...xn) = v
% 0.21/0.55 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.55 variables of u and v.
% 0.21/0.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.55 input problem has no model of domain size 1).
% 0.21/0.55
% 0.21/0.55 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.55
% 0.21/0.55 Axiom 1 (v3_down): fresh8(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 0.21/0.55 Axiom 2 (v3_down): fresh8(state(X, Y, Z, v3(W, V), U, T, S, X2, Y2, Z2, e1(s(s(W)), V), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, v3(s(W), V), U, T, S, X2, Y2, Z2, e1(W, V), W2).
% 0.21/0.55 Axiom 3 (initial_state): state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), o), e2(s(s(s(s(o)))), s(s(s(o))))) = true2.
% 0.21/0.55
% 0.21/0.55 Goal 1 (goal_state): state(X, Y, Z, v3(s(s(s(o))), o), W, V, U, T, S, X2, Y2, Z2) = true2.
% 0.21/0.55 The goal is true when:
% 0.21/0.55 X = bb(o, s(o))
% 0.21/0.55 Y = v1(o, o)
% 0.21/0.55 Z = v2(o, s(s(s(o))))
% 0.21/0.55 W = v4(s(s(o)), s(s(s(o))))
% 0.21/0.55 V = h(s(s(o)), s(o))
% 0.21/0.55 U = s1(s(s(s(o))), s(o))
% 0.21/0.55 T = s2(s(s(s(o))), s(s(o)))
% 0.21/0.55 S = s3(s(s(s(s(o)))), s(o))
% 0.21/0.55 X2 = s4(s(s(s(s(o)))), s(s(o)))
% 0.21/0.55 Y2 = e1(s(s(o)), o)
% 0.21/0.55 Z2 = e2(s(s(s(s(o)))), s(s(s(o))))
% 0.21/0.55
% 0.21/0.55 Proof:
% 0.21/0.55 state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(s(o)))), s(s(s(o)))))
% 0.21/0.55 = { by axiom 2 (v3_down) R->L }
% 0.21/0.55 fresh8(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), o), e2(s(s(s(s(o)))), s(s(s(o))))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(o)), o, v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(s(s(o)))))
% 0.21/0.55 = { by axiom 3 (initial_state) }
% 0.21/0.55 fresh8(true2, true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(o)), o, v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(s(s(o)))))
% 0.21/0.55 = { by axiom 1 (v3_down) }
% 0.21/0.55 true2
% 0.21/0.55 % SZS output end Proof
% 0.21/0.55
% 0.21/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
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