TSTP Solution File: SWV174+1 by Twee---2.5.0
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% File : Twee---2.5.0
% Problem : SWV174+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n026.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 : Mon Jun 24 17:31:07 EDT 2024
% Result : Theorem 4.11s 0.89s
% Output : Proof 4.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV174+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n026.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 : Thu Jun 20 18:06:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 4.11/0.89 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 4.11/0.89
% 4.11/0.89 % SZS status Theorem
% 4.11/0.89
% 4.11/0.90 % SZS output start Proof
% 4.11/0.90 Take the following subset of the input axioms:
% 4.11/0.90 fof(cl5_nebula_init_0046, conjecture, (leq(n0, pv10) & (leq(pv10, n135299) & (![A2]: ((leq(n0, A2) & leq(A2, pred(pv10))) => ![B]: ((leq(n0, B) & leq(B, n4)) => a_select3(q_init, A2, B)=init)) & ![C]: ((leq(n0, C) & leq(C, n4)) => a_select3(center_init, C, n0)=init)))) => ![D, E]: ((leq(n0, D) & (leq(n0, E) & (leq(D, n135299) & leq(E, n4)))) => (gt(pv10, D) => a_select3(q_init, D, E)=init))).
% 4.11/0.90 fof(leq_gt_pred, axiom, ![X, Y]: (leq(X, pred(Y)) <=> gt(Y, X))).
% 4.11/0.90
% 4.11/0.90 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.11/0.90 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.11/0.90 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.11/0.90 fresh(y, y, x1...xn) = u
% 4.11/0.90 C => fresh(s, t, x1...xn) = v
% 4.11/0.90 where fresh is a fresh function symbol and x1..xn are the free
% 4.11/0.90 variables of u and v.
% 4.11/0.90 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.11/0.90 input problem has no model of domain size 1).
% 4.11/0.90
% 4.11/0.90 The encoding turns the above axioms into the following unit equations and goals:
% 4.11/0.90
% 4.11/0.90 Axiom 1 (cl5_nebula_init_0046_3): leq(n0, d) = true3.
% 4.11/0.90 Axiom 2 (cl5_nebula_init_0046_2): leq(n0, e) = true3.
% 4.11/0.90 Axiom 3 (cl5_nebula_init_0046_5): leq(e, n4) = true3.
% 4.11/0.90 Axiom 4 (cl5_nebula_init_0046): gt(pv10, d) = true3.
% 4.11/0.90 Axiom 5 (cl5_nebula_init_0046_8): fresh46(X, X, Y, Z) = a_select3(q_init, Y, Z).
% 4.11/0.90 Axiom 6 (cl5_nebula_init_0046_8): fresh43(X, X, Y, Z) = init.
% 4.11/0.90 Axiom 7 (leq_gt_pred): fresh35(X, X, Y, Z) = true3.
% 4.11/0.90 Axiom 8 (cl5_nebula_init_0046_8): fresh45(X, X, Y, Z) = fresh46(leq(Z, n4), true3, Y, Z).
% 4.11/0.90 Axiom 9 (cl5_nebula_init_0046_8): fresh44(X, X, Y, Z) = fresh45(leq(n0, Y), true3, Y, Z).
% 4.11/0.90 Axiom 10 (leq_gt_pred): fresh35(gt(X, Y), true3, Y, X) = leq(Y, pred(X)).
% 4.11/0.90 Axiom 11 (cl5_nebula_init_0046_8): fresh44(leq(n0, X), true3, Y, X) = fresh43(leq(Y, pred(pv10)), true3, Y, X).
% 4.11/0.90
% 4.11/0.90 Goal 1 (cl5_nebula_init_0046_7): a_select3(q_init, d, e) = init.
% 4.11/0.90 Proof:
% 4.11/0.90 a_select3(q_init, d, e)
% 4.11/0.90 = { by axiom 5 (cl5_nebula_init_0046_8) R->L }
% 4.11/0.90 fresh46(true3, true3, d, e)
% 4.11/0.90 = { by axiom 3 (cl5_nebula_init_0046_5) R->L }
% 4.11/0.90 fresh46(leq(e, n4), true3, d, e)
% 4.11/0.90 = { by axiom 8 (cl5_nebula_init_0046_8) R->L }
% 4.11/0.90 fresh45(true3, true3, d, e)
% 4.11/0.90 = { by axiom 1 (cl5_nebula_init_0046_3) R->L }
% 4.11/0.90 fresh45(leq(n0, d), true3, d, e)
% 4.11/0.90 = { by axiom 9 (cl5_nebula_init_0046_8) R->L }
% 4.11/0.90 fresh44(true3, true3, d, e)
% 4.11/0.90 = { by axiom 2 (cl5_nebula_init_0046_2) R->L }
% 4.11/0.90 fresh44(leq(n0, e), true3, d, e)
% 4.11/0.90 = { by axiom 11 (cl5_nebula_init_0046_8) }
% 4.11/0.90 fresh43(leq(d, pred(pv10)), true3, d, e)
% 4.11/0.90 = { by axiom 10 (leq_gt_pred) R->L }
% 4.11/0.90 fresh43(fresh35(gt(pv10, d), true3, d, pv10), true3, d, e)
% 4.11/0.90 = { by axiom 4 (cl5_nebula_init_0046) }
% 4.11/0.90 fresh43(fresh35(true3, true3, d, pv10), true3, d, e)
% 4.11/0.90 = { by axiom 7 (leq_gt_pred) }
% 4.11/0.90 fresh43(true3, true3, d, e)
% 4.11/0.90 = { by axiom 6 (cl5_nebula_init_0046_8) }
% 4.11/0.90 init
% 4.11/0.90 % SZS output end Proof
% 4.11/0.90
% 4.11/0.90 RESULT: Theorem (the conjecture is true).
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