TSTP Solution File: SWV164+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV164+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 : n006.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 23:02:49 EDT 2023
% Result : Theorem 1.52s 0.62s
% Output : Proof 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV164+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 09:42:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.52/0.62 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.52/0.62
% 1.52/0.62 % SZS status Theorem
% 1.52/0.62
% 1.52/0.62 % SZS output start Proof
% 1.52/0.62 Take the following subset of the input axioms:
% 1.52/0.62 fof(cl5_nebula_norm_0014, conjecture, (leq(n0, pv10) & (leq(pv10, n135299) & ![A2]: ((leq(n0, A2) & leq(A2, pred(pv10))) => sum(n0, n4, a_select3(q, A2, tptp_sum_index))=n1))) => ![B]: ((leq(n0, B) & leq(B, tptp_minus_1)) => a_select3(q, pv10, B)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))))).
% 1.52/0.62 fof(finite_domain_0, axiom, ![X]: ((leq(n0, X) & leq(X, n0)) => X=n0)).
% 1.52/0.62 fof(irreflexivity_gt, axiom, ![X2]: ~gt(X2, X2)).
% 1.52/0.62 fof(leq_succ, axiom, ![Y, X2]: (leq(X2, Y) => leq(X2, succ(Y)))).
% 1.52/0.63 fof(leq_succ_gt_equiv, axiom, ![X2, Y2]: (leq(X2, Y2) <=> gt(succ(Y2), X2))).
% 1.52/0.63 fof(matrix_symm_joseph_update, axiom, ![C, N, M, D, E, F, B2, A2_2]: ((![I, J]: ((leq(n0, I) & (leq(I, M) & (leq(n0, J) & leq(J, M)))) => a_select3(D, I, J)=a_select3(D, 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(F, I2, J2)=a_select3(F, 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(C, tptp_mmul(D, trans(C))), tptp_mmul(E, tptp_mmul(F, trans(E)))), trans(B2)))), I2, J2)=a_select3(tptp_madd(A2_2, tptp_mmul(B2, tptp_mmul(tptp_madd(tptp_mmul(C, tptp_mmul(D, trans(C))), tptp_mmul(E, tptp_mmul(F, trans(E)))), trans(B2)))), J2, I2)))).
% 1.52/0.63 fof(succ_tptp_minus_1, axiom, succ(tptp_minus_1)=n0).
% 1.52/0.63
% 1.52/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.52/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.52/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.52/0.63 fresh(y, y, x1...xn) = u
% 1.52/0.63 C => fresh(s, t, x1...xn) = v
% 1.52/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 1.52/0.63 variables of u and v.
% 1.52/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.52/0.63 input problem has no model of domain size 1).
% 1.52/0.63
% 1.52/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 1.52/0.63
% 1.52/0.63 Axiom 1 (succ_tptp_minus_1): succ(tptp_minus_1) = n0.
% 1.52/0.63 Axiom 2 (cl5_nebula_norm_0014_1): leq(n0, b) = true3.
% 1.52/0.63 Axiom 3 (cl5_nebula_norm_0014_3): leq(b, tptp_minus_1) = true3.
% 1.52/0.63 Axiom 4 (finite_domain_0): fresh(X, X, Y) = Y.
% 1.52/0.63 Axiom 5 (finite_domain_0): fresh39(X, X, Y) = n0.
% 1.52/0.63 Axiom 6 (leq_succ): fresh32(X, X, Y, Z) = true3.
% 1.52/0.63 Axiom 7 (leq_succ_gt_equiv_1): fresh29(X, X, Y, Z) = true3.
% 1.52/0.63 Axiom 8 (finite_domain_0): fresh(leq(n0, X), true3, X) = fresh39(leq(X, n0), true3, X).
% 1.52/0.63 Axiom 9 (leq_succ): fresh32(leq(X, Y), true3, X, Y) = leq(X, succ(Y)).
% 1.52/0.63 Axiom 10 (leq_succ_gt_equiv_1): fresh29(leq(X, Y), true3, X, Y) = gt(succ(Y), X).
% 1.52/0.63
% 1.52/0.63 Goal 1 (irreflexivity_gt): gt(X, X) = true3.
% 1.52/0.63 The goal is true when:
% 1.52/0.63 X = n0
% 1.52/0.63
% 1.52/0.63 Proof:
% 1.52/0.63 gt(n0, n0)
% 1.52/0.63 = { by axiom 5 (finite_domain_0) R->L }
% 1.52/0.63 gt(n0, fresh39(true3, true3, b))
% 1.52/0.63 = { by axiom 6 (leq_succ) R->L }
% 1.52/0.63 gt(n0, fresh39(fresh32(true3, true3, b, tptp_minus_1), true3, b))
% 1.52/0.63 = { by axiom 3 (cl5_nebula_norm_0014_3) R->L }
% 1.52/0.63 gt(n0, fresh39(fresh32(leq(b, tptp_minus_1), true3, b, tptp_minus_1), true3, b))
% 1.52/0.63 = { by axiom 9 (leq_succ) }
% 1.52/0.63 gt(n0, fresh39(leq(b, succ(tptp_minus_1)), true3, b))
% 1.52/0.63 = { by axiom 1 (succ_tptp_minus_1) }
% 1.52/0.63 gt(n0, fresh39(leq(b, n0), true3, b))
% 1.52/0.63 = { by axiom 8 (finite_domain_0) R->L }
% 1.52/0.63 gt(n0, fresh(leq(n0, b), true3, b))
% 1.52/0.63 = { by axiom 2 (cl5_nebula_norm_0014_1) }
% 1.52/0.63 gt(n0, fresh(true3, true3, b))
% 1.52/0.63 = { by axiom 4 (finite_domain_0) }
% 1.52/0.63 gt(n0, b)
% 1.52/0.63 = { by axiom 1 (succ_tptp_minus_1) R->L }
% 1.52/0.63 gt(succ(tptp_minus_1), b)
% 1.52/0.63 = { by axiom 10 (leq_succ_gt_equiv_1) R->L }
% 1.52/0.63 fresh29(leq(b, tptp_minus_1), true3, b, tptp_minus_1)
% 1.52/0.63 = { by axiom 3 (cl5_nebula_norm_0014_3) }
% 1.52/0.63 fresh29(true3, true3, b, tptp_minus_1)
% 1.52/0.63 = { by axiom 7 (leq_succ_gt_equiv_1) }
% 1.52/0.63 true3
% 1.52/0.63 % SZS output end Proof
% 1.52/0.63
% 1.52/0.63 RESULT: Theorem (the conjecture is true).
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