TSTP Solution File: SWV188+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV188+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 : n028.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 23:02:55 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV188+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 04:27:25 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.64 Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.64
% 0.21/0.64 % SZS status Theorem
% 0.21/0.64
% 0.21/0.65 % SZS output start Proof
% 0.21/0.65 Take the following subset of the input axioms:
% 0.21/0.65 fof(cl5_nebula_init_0116, conjecture, (![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_select2(rho_init, C)=init) & (![D]: ((leq(n0, D) & leq(D, n4)) => a_select3(center_init, D, n0)=init) & ((gt(loopcounter, n1) => ![E]: ((leq(n0, E) & leq(E, n4)) => a_select2(muold_init, E)=init)) & ((gt(loopcounter, n1) => ![F]: ((leq(n0, F) & leq(F, n4)) => a_select2(rhoold_init, F)=init)) & (gt(loopcounter, n1) => ![G]: ((leq(n0, G) & leq(G, n4)) => a_select2(sigmaold_init, G)=init))))))) => ![H]: ((leq(n0, H) & leq(H, tptp_minus_1)) => a_select2(mu_init, H)=init)).
% 0.21/0.65 fof(finite_domain_0, axiom, ![X]: ((leq(n0, X) & leq(X, n0)) => X=n0)).
% 0.21/0.65 fof(irreflexivity_gt, axiom, ![X2]: ~gt(X2, X2)).
% 0.21/0.65 fof(leq_succ, axiom, ![Y, X2]: (leq(X2, Y) => leq(X2, succ(Y)))).
% 0.21/0.65 fof(leq_succ_gt_equiv, axiom, ![X2, Y2]: (leq(X2, Y2) <=> gt(succ(Y2), X2))).
% 0.21/0.65 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)))).
% 0.21/0.65 fof(succ_tptp_minus_1, axiom, succ(tptp_minus_1)=n0).
% 0.21/0.65 fof(sum_plus_base, axiom, ![Body]: sum(n0, tptp_minus_1, Body)=n0).
% 0.21/0.65 fof(sum_plus_base_float, axiom, ![Body2]: tptp_float_0_0=sum(n0, tptp_minus_1, Body2)).
% 0.21/0.65 fof(ttrue, axiom, true).
% 0.21/0.65
% 0.21/0.65 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.65 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.65 fresh(y, y, x1...xn) = u
% 0.21/0.65 C => fresh(s, t, x1...xn) = v
% 0.21/0.65 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.65 variables of u and v.
% 0.21/0.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.65 input problem has no model of domain size 1).
% 0.21/0.65
% 0.21/0.65 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.65
% 0.21/0.65 Axiom 1 (ttrue): true = true3.
% 0.21/0.65 Axiom 2 (succ_tptp_minus_1): succ(tptp_minus_1) = n0.
% 0.21/0.65 Axiom 3 (cl5_nebula_init_0116_1): leq(h, tptp_minus_1) = true3.
% 0.21/0.65 Axiom 4 (cl5_nebula_init_0116): leq(n0, h) = true3.
% 0.21/0.65 Axiom 5 (sum_plus_base_float): tptp_float_0_0 = sum(n0, tptp_minus_1, X).
% 0.21/0.65 Axiom 6 (sum_plus_base): sum(n0, tptp_minus_1, X) = n0.
% 0.21/0.65 Axiom 7 (finite_domain_0): fresh(X, X, Y) = Y.
% 0.21/0.65 Axiom 8 (finite_domain_0): fresh39(X, X, Y) = n0.
% 0.21/0.65 Axiom 9 (leq_succ): fresh32(X, X, Y, Z) = true3.
% 0.21/0.65 Axiom 10 (leq_succ_gt_equiv_1): fresh29(X, X, Y, Z) = true3.
% 0.21/0.65 Axiom 11 (finite_domain_0): fresh(leq(n0, X), true3, X) = fresh39(leq(X, n0), true3, X).
% 0.21/0.65 Axiom 12 (leq_succ): fresh32(leq(X, Y), true3, X, Y) = leq(X, succ(Y)).
% 0.21/0.65 Axiom 13 (leq_succ_gt_equiv_1): fresh29(leq(X, Y), true3, X, Y) = gt(succ(Y), X).
% 0.21/0.65
% 0.21/0.65 Lemma 14: n0 = tptp_float_0_0.
% 0.21/0.65 Proof:
% 0.21/0.65 n0
% 0.21/0.65 = { by axiom 6 (sum_plus_base) R->L }
% 0.21/0.65 sum(n0, tptp_minus_1, X)
% 0.21/0.65 = { by axiom 5 (sum_plus_base_float) R->L }
% 0.21/0.65 tptp_float_0_0
% 0.21/0.65
% 0.21/0.65 Lemma 15: leq(h, tptp_minus_1) = true.
% 0.21/0.65 Proof:
% 0.21/0.65 leq(h, tptp_minus_1)
% 0.21/0.65 = { by axiom 3 (cl5_nebula_init_0116_1) }
% 0.21/0.65 true3
% 0.21/0.65 = { by axiom 1 (ttrue) R->L }
% 0.21/0.65 true
% 0.21/0.65
% 0.21/0.65 Goal 1 (irreflexivity_gt): gt(X, X) = true3.
% 0.21/0.65 The goal is true when:
% 0.21/0.65 X = tptp_float_0_0
% 0.21/0.65
% 0.21/0.65 Proof:
% 0.21/0.65 gt(tptp_float_0_0, tptp_float_0_0)
% 0.21/0.65 = { by lemma 14 R->L }
% 0.21/0.65 gt(tptp_float_0_0, n0)
% 0.21/0.65 = { by axiom 8 (finite_domain_0) R->L }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(true, true, h))
% 0.21/0.65 = { by axiom 1 (ttrue) }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(true3, true, h))
% 0.21/0.65 = { by axiom 9 (leq_succ) R->L }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(fresh32(true, true, h, tptp_minus_1), true, h))
% 0.21/0.65 = { by lemma 15 R->L }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(fresh32(leq(h, tptp_minus_1), true, h, tptp_minus_1), true, h))
% 0.21/0.65 = { by axiom 1 (ttrue) }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(fresh32(leq(h, tptp_minus_1), true3, h, tptp_minus_1), true, h))
% 0.21/0.65 = { by axiom 12 (leq_succ) }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(leq(h, succ(tptp_minus_1)), true, h))
% 0.21/0.65 = { by axiom 2 (succ_tptp_minus_1) }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(leq(h, n0), true, h))
% 0.21/0.65 = { by lemma 14 }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(leq(h, tptp_float_0_0), true, h))
% 0.21/0.65 = { by axiom 1 (ttrue) }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(leq(h, tptp_float_0_0), true3, h))
% 0.21/0.65 = { by lemma 14 R->L }
% 0.21/0.65 gt(tptp_float_0_0, fresh39(leq(h, n0), true3, h))
% 0.21/0.65 = { by axiom 11 (finite_domain_0) R->L }
% 0.21/0.65 gt(tptp_float_0_0, fresh(leq(n0, h), true3, h))
% 0.21/0.65 = { by lemma 14 }
% 0.21/0.65 gt(tptp_float_0_0, fresh(leq(tptp_float_0_0, h), true3, h))
% 0.21/0.65 = { by axiom 1 (ttrue) R->L }
% 0.21/0.65 gt(tptp_float_0_0, fresh(leq(tptp_float_0_0, h), true, h))
% 0.21/0.65 = { by lemma 14 R->L }
% 0.21/0.65 gt(tptp_float_0_0, fresh(leq(n0, h), true, h))
% 0.21/0.65 = { by axiom 4 (cl5_nebula_init_0116) }
% 0.21/0.65 gt(tptp_float_0_0, fresh(true3, true, h))
% 0.21/0.65 = { by axiom 1 (ttrue) R->L }
% 0.21/0.65 gt(tptp_float_0_0, fresh(true, true, h))
% 0.21/0.65 = { by axiom 7 (finite_domain_0) }
% 0.21/0.65 gt(tptp_float_0_0, h)
% 0.21/0.65 = { by lemma 14 R->L }
% 0.21/0.65 gt(n0, h)
% 0.21/0.65 = { by axiom 2 (succ_tptp_minus_1) R->L }
% 0.21/0.65 gt(succ(tptp_minus_1), h)
% 0.21/0.65 = { by axiom 13 (leq_succ_gt_equiv_1) R->L }
% 0.21/0.65 fresh29(leq(h, tptp_minus_1), true3, h, tptp_minus_1)
% 0.21/0.65 = { by axiom 1 (ttrue) R->L }
% 0.21/0.65 fresh29(leq(h, tptp_minus_1), true, h, tptp_minus_1)
% 0.21/0.65 = { by lemma 15 }
% 0.21/0.65 fresh29(true, true, h, tptp_minus_1)
% 0.21/0.65 = { by axiom 10 (leq_succ_gt_equiv_1) }
% 0.21/0.65 true3
% 0.21/0.65 = { by axiom 1 (ttrue) R->L }
% 0.21/0.65 true
% 0.21/0.65 = { by axiom 1 (ttrue) }
% 0.21/0.65 true3
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65
% 0.21/0.65 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------