TSTP Solution File: SWV181+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : n024.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 23:02:53 EDT 2023
% Result : Theorem 3.43s 0.82s
% Output : Proof 3.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 06:15:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.43/0.82 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.43/0.82
% 3.43/0.82 % SZS status Theorem
% 3.43/0.82
% 3.43/0.82 % SZS output start Proof
% 3.43/0.82 Take the following subset of the input axioms:
% 3.43/0.83 fof(cl5_nebula_init_0081, conjecture, (leq(tptp_float_0_001, pv76) & (leq(n1, loopcounter) & (gt(n1, loopcounter) & (![A2]: ((leq(n0, A2) & leq(A2, n135299)) => ![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) & ((gt(loopcounter, n0) => ![D]: ((leq(n0, D) & leq(D, n4)) => a_select2(mu_init, D)=init)) & ((gt(loopcounter, n0) => ![E]: ((leq(n0, E) & leq(E, n4)) => a_select2(rho_init, E)=init)) & (gt(loopcounter, n0) => ![F]: ((leq(n0, F) & leq(F, n4)) => a_select2(sigma_init, F)=init))))))))) => ![G]: ((leq(n0, G) & leq(G, n4)) => a_select2(muold_init, G)=init)).
% 3.43/0.83 fof(finite_domain_0, axiom, ![X]: ((leq(n0, X) & leq(X, n0)) => X=n0)).
% 3.43/0.83 fof(gt_1_0, axiom, gt(n1, n0)).
% 3.43/0.83 fof(irreflexivity_gt, axiom, ![X2]: ~gt(X2, X2)).
% 3.43/0.83 fof(leq_gt1, axiom, ![Y, X2]: (gt(Y, X2) => leq(X2, Y))).
% 3.43/0.83 fof(leq_gt_pred, axiom, ![X2, Y2]: (leq(X2, pred(Y2)) <=> gt(Y2, X2))).
% 3.43/0.83 fof(leq_succ_gt, axiom, ![X2, Y2]: (leq(succ(X2), Y2) => gt(Y2, X2))).
% 3.43/0.83 fof(leq_succ_gt_equiv, axiom, ![X2, Y2]: (leq(X2, Y2) <=> gt(succ(Y2), X2))).
% 3.43/0.83 fof(matrix_symm_joseph_update, axiom, ![N, M, C2, B2, D2, E2, F2, A2_2]: ((![I, J]: ((leq(n0, I) & (leq(I, M) & (leq(n0, J) & leq(J, M)))) => a_select3(D2, I, J)=a_select3(D2, J, I)) & (![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(A2_2, I2, J2)=a_select3(A2_2, J2, I2)) & ![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(F2, I2, J2)=a_select3(F2, J2, I2)))) => ![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(tptp_madd(A2_2, tptp_mmul(B2, tptp_mmul(tptp_madd(tptp_mmul(C2, tptp_mmul(D2, trans(C2))), tptp_mmul(E2, tptp_mmul(F2, trans(E2)))), trans(B2)))), I2, J2)=a_select3(tptp_madd(A2_2, tptp_mmul(B2, tptp_mmul(tptp_madd(tptp_mmul(C2, tptp_mmul(D2, trans(C2))), tptp_mmul(E2, tptp_mmul(F2, trans(E2)))), trans(B2)))), J2, I2)))).
% 3.43/0.83 fof(pred_succ, axiom, ![X2]: pred(succ(X2))=X2).
% 3.43/0.83 fof(reflexivity_leq, axiom, ![X2]: leq(X2, X2)).
% 3.43/0.83 fof(successor_1, axiom, succ(n0)=n1).
% 3.43/0.83 fof(transitivity_leq, axiom, ![Z, X2, Y2]: ((leq(X2, Y2) & leq(Y2, Z)) => leq(X2, Z))).
% 3.43/0.83
% 3.43/0.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.43/0.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.43/0.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.43/0.83 fresh(y, y, x1...xn) = u
% 3.43/0.83 C => fresh(s, t, x1...xn) = v
% 3.43/0.83 where fresh is a fresh function symbol and x1..xn are the free
% 3.43/0.83 variables of u and v.
% 3.43/0.83 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.43/0.83 input problem has no model of domain size 1).
% 3.43/0.83
% 3.43/0.83 The encoding turns the above axioms into the following unit equations and goals:
% 3.43/0.83
% 3.43/0.83 Axiom 1 (successor_1): succ(n0) = n1.
% 3.43/0.83 Axiom 2 (reflexivity_leq): leq(X, X) = true3.
% 3.43/0.83 Axiom 3 (cl5_nebula_init_0081_2): leq(n1, loopcounter) = true3.
% 3.43/0.83 Axiom 4 (gt_1_0): gt(n1, n0) = true3.
% 3.43/0.83 Axiom 5 (cl5_nebula_init_0081): gt(n1, loopcounter) = true3.
% 3.43/0.83 Axiom 6 (pred_succ): pred(succ(X)) = X.
% 3.43/0.83 Axiom 7 (finite_domain_0): fresh(X, X, Y) = Y.
% 3.43/0.83 Axiom 8 (finite_domain_0): fresh39(X, X, Y) = n0.
% 3.43/0.83 Axiom 9 (leq_gt1): fresh36(X, X, Y, Z) = true3.
% 3.43/0.83 Axiom 10 (leq_gt_pred): fresh35(X, X, Y, Z) = true3.
% 3.43/0.83 Axiom 11 (leq_succ_gt): fresh31(X, X, Y, Z) = true3.
% 3.43/0.83 Axiom 12 (leq_succ_gt_equiv_1): fresh29(X, X, Y, Z) = true3.
% 3.43/0.83 Axiom 13 (transitivity_leq): fresh7(X, X, Y, Z) = true3.
% 3.43/0.83 Axiom 14 (finite_domain_0): fresh(leq(n0, X), true3, X) = fresh39(leq(X, n0), true3, X).
% 3.43/0.83 Axiom 15 (transitivity_leq): fresh8(X, X, Y, Z, W) = leq(Y, W).
% 3.43/0.83 Axiom 16 (leq_gt1): fresh36(gt(X, Y), true3, Y, X) = leq(Y, X).
% 3.43/0.83 Axiom 17 (leq_gt_pred): fresh35(gt(X, Y), true3, Y, X) = leq(Y, pred(X)).
% 3.43/0.83 Axiom 18 (leq_succ_gt_equiv_1): fresh29(leq(X, Y), true3, X, Y) = gt(succ(Y), X).
% 3.43/0.83 Axiom 19 (leq_succ_gt): fresh31(leq(succ(X), Y), true3, X, Y) = gt(Y, X).
% 3.43/0.83 Axiom 20 (transitivity_leq): fresh8(leq(X, Y), true3, Z, X, Y) = fresh7(leq(Z, X), true3, Z, Y).
% 3.43/0.83
% 3.43/0.83 Lemma 21: loopcounter = n0.
% 3.43/0.83 Proof:
% 3.43/0.83 loopcounter
% 3.43/0.83 = { by axiom 7 (finite_domain_0) R->L }
% 3.43/0.83 fresh(true3, true3, loopcounter)
% 3.43/0.83 = { by axiom 9 (leq_gt1) R->L }
% 3.43/0.83 fresh(fresh36(true3, true3, n0, loopcounter), true3, loopcounter)
% 3.43/0.83 = { by axiom 11 (leq_succ_gt) R->L }
% 3.43/0.83 fresh(fresh36(fresh31(true3, true3, n0, loopcounter), true3, n0, loopcounter), true3, loopcounter)
% 3.43/0.83 = { by axiom 3 (cl5_nebula_init_0081_2) R->L }
% 3.43/0.83 fresh(fresh36(fresh31(leq(n1, loopcounter), true3, n0, loopcounter), true3, n0, loopcounter), true3, loopcounter)
% 3.43/0.83 = { by axiom 1 (successor_1) R->L }
% 3.43/0.83 fresh(fresh36(fresh31(leq(succ(n0), loopcounter), true3, n0, loopcounter), true3, n0, loopcounter), true3, loopcounter)
% 3.43/0.83 = { by axiom 19 (leq_succ_gt) }
% 3.43/0.83 fresh(fresh36(gt(loopcounter, n0), true3, n0, loopcounter), true3, loopcounter)
% 3.43/0.83 = { by axiom 16 (leq_gt1) }
% 3.43/0.83 fresh(leq(n0, loopcounter), true3, loopcounter)
% 3.43/0.83 = { by axiom 14 (finite_domain_0) }
% 3.43/0.83 fresh39(leq(loopcounter, n0), true3, loopcounter)
% 3.43/0.83 = { by axiom 6 (pred_succ) R->L }
% 3.43/0.83 fresh39(leq(loopcounter, pred(succ(n0))), true3, loopcounter)
% 3.43/0.83 = { by axiom 1 (successor_1) }
% 3.43/0.83 fresh39(leq(loopcounter, pred(n1)), true3, loopcounter)
% 3.43/0.83 = { by axiom 17 (leq_gt_pred) R->L }
% 3.43/0.83 fresh39(fresh35(gt(n1, loopcounter), true3, loopcounter, n1), true3, loopcounter)
% 3.43/0.83 = { by axiom 5 (cl5_nebula_init_0081) }
% 3.43/0.83 fresh39(fresh35(true3, true3, loopcounter, n1), true3, loopcounter)
% 3.43/0.83 = { by axiom 10 (leq_gt_pred) }
% 3.43/0.83 fresh39(true3, true3, loopcounter)
% 3.43/0.83 = { by axiom 8 (finite_domain_0) }
% 3.43/0.83 n0
% 3.43/0.83
% 3.43/0.83 Lemma 22: leq(n1, n0) = true3.
% 3.43/0.83 Proof:
% 3.43/0.83 leq(n1, n0)
% 3.43/0.83 = { by lemma 21 R->L }
% 3.43/0.83 leq(n1, loopcounter)
% 3.43/0.83 = { by axiom 15 (transitivity_leq) R->L }
% 3.43/0.83 fresh8(true3, true3, n1, n1, loopcounter)
% 3.43/0.83 = { by axiom 3 (cl5_nebula_init_0081_2) R->L }
% 3.43/0.83 fresh8(leq(n1, loopcounter), true3, n1, n1, loopcounter)
% 3.43/0.83 = { by axiom 20 (transitivity_leq) }
% 3.43/0.83 fresh7(leq(n1, n1), true3, n1, loopcounter)
% 3.43/0.83 = { by lemma 21 }
% 3.43/0.83 fresh7(leq(n1, n1), true3, n1, n0)
% 3.43/0.83 = { by axiom 2 (reflexivity_leq) }
% 3.43/0.83 fresh7(true3, true3, n1, n0)
% 3.43/0.83 = { by axiom 13 (transitivity_leq) }
% 3.43/0.83 true3
% 3.43/0.83
% 3.43/0.83 Lemma 23: n1 = n0.
% 3.43/0.83 Proof:
% 3.43/0.83 n1
% 3.43/0.83 = { by axiom 7 (finite_domain_0) R->L }
% 3.43/0.83 fresh(true3, true3, n1)
% 3.43/0.83 = { by axiom 9 (leq_gt1) R->L }
% 3.43/0.83 fresh(fresh36(true3, true3, n0, n1), true3, n1)
% 3.43/0.83 = { by axiom 4 (gt_1_0) R->L }
% 3.43/0.83 fresh(fresh36(gt(n1, n0), true3, n0, n1), true3, n1)
% 3.43/0.83 = { by axiom 16 (leq_gt1) }
% 3.43/0.83 fresh(leq(n0, n1), true3, n1)
% 3.43/0.83 = { by axiom 14 (finite_domain_0) }
% 3.43/0.83 fresh39(leq(n1, n0), true3, n1)
% 3.43/0.83 = { by lemma 22 }
% 3.43/0.83 fresh39(true3, true3, n1)
% 3.43/0.83 = { by axiom 8 (finite_domain_0) }
% 3.43/0.83 n0
% 3.43/0.83
% 3.43/0.83 Goal 1 (irreflexivity_gt): gt(X, X) = true3.
% 3.43/0.83 The goal is true when:
% 3.43/0.83 X = n0
% 3.43/0.83
% 3.43/0.83 Proof:
% 3.43/0.83 gt(n0, n0)
% 3.43/0.83 = { by lemma 23 R->L }
% 3.43/0.83 gt(n1, n0)
% 3.43/0.83 = { by lemma 23 R->L }
% 3.43/0.83 gt(n1, n1)
% 3.43/0.83 = { by axiom 1 (successor_1) R->L }
% 3.43/0.83 gt(succ(n0), n1)
% 3.43/0.83 = { by axiom 18 (leq_succ_gt_equiv_1) R->L }
% 3.43/0.83 fresh29(leq(n1, n0), true3, n1, n0)
% 3.43/0.83 = { by lemma 22 }
% 3.43/0.83 fresh29(true3, true3, n1, n0)
% 3.43/0.83 = { by axiom 12 (leq_succ_gt_equiv_1) }
% 3.43/0.83 true3
% 3.43/0.83 % SZS output end Proof
% 3.43/0.83
% 3.43/0.83 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------