TSTP Solution File: SWV160+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV160+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 : n004.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 23:02:48 EDT 2023
% Result : Theorem 0.19s 0.64s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 06:31:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.64 Command-line arguments: --no-flatten-goal
% 0.19/0.64
% 0.19/0.64 % SZS status Theorem
% 0.19/0.64
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 Take the following subset of the input axioms:
% 0.19/0.65 fof(cl5_nebula_norm_0010, conjecture, (pv84=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)))) & (leq(n0, pv10) & (leq(n0, pv47) & (leq(pv10, n135299) & (leq(pv47, n4) & (![A2]: ((leq(n0, A2) & leq(A2, pred(pv47))) => a_select3(q, pv10, A2)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, A2)), minus(a_select2(x, pv10), a_select2(mu, A2))), tptp_minus_2), times(a_select2(sigma, A2), a_select2(sigma, A2)))), a_select2(rho, A2)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, A2))), 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)))))) & ![B]: ((leq(n0, B) & leq(B, pred(pv10))) => sum(n0, n4, a_select3(q, B, tptp_sum_index))=n1))))))) => ![C]: ((leq(n0, C) & leq(C, pred(pv10))) => (pv10=C => sum(n0, n4, cond(tptp_term_equals(pv47, tptp_sum_index), divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, pv47)), minus(a_select2(x, pv10), a_select2(mu, pv47))), tptp_minus_2), times(a_select2(sigma, pv47), a_select2(sigma, pv47)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), pv84), a_select3(q, C, tptp_sum_index)))=n1))).
% 0.19/0.65 fof(irreflexivity_gt, axiom, ![X]: ~gt(X, X)).
% 0.19/0.65 fof(leq_succ_gt_equiv, axiom, ![Y, X2]: (leq(X2, Y) <=> gt(succ(Y), X2))).
% 0.19/0.65 fof(matrix_symm_joseph_update, axiom, ![N, M, D, E, F, C2, 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(C2, tptp_mmul(D, trans(C2))), 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(C2, tptp_mmul(D, trans(C2))), tptp_mmul(E, tptp_mmul(F, trans(E)))), trans(B2)))), J2, I2)))).
% 0.19/0.65 fof(succ_pred, axiom, ![X2]: succ(pred(X2))=X2).
% 0.19/0.65 fof(ttrue, axiom, true).
% 0.19/0.65
% 0.19/0.65 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.65 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.65 fresh(y, y, x1...xn) = u
% 0.19/0.65 C => fresh(s, t, x1...xn) = v
% 0.19/0.65 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.65 variables of u and v.
% 0.19/0.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.65 input problem has no model of domain size 1).
% 0.19/0.65
% 0.19/0.65 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.65
% 0.19/0.65 Axiom 1 (cl5_nebula_norm_0010_1): pv10 = c.
% 0.19/0.65 Axiom 2 (ttrue): true = true3.
% 0.19/0.65 Axiom 3 (succ_pred): succ(pred(X)) = X.
% 0.19/0.65 Axiom 4 (cl5_nebula_norm_0010_7): leq(c, pred(pv10)) = true3.
% 0.19/0.65 Axiom 5 (leq_succ_gt_equiv_1): fresh29(X, X, Y, Z) = true3.
% 0.19/0.65 Axiom 6 (leq_succ_gt_equiv_1): fresh29(leq(X, Y), true3, X, Y) = gt(succ(Y), X).
% 0.19/0.65
% 0.19/0.65 Goal 1 (irreflexivity_gt): gt(X, X) = true3.
% 0.19/0.65 The goal is true when:
% 0.19/0.65 X = c
% 0.19/0.65
% 0.19/0.65 Proof:
% 0.19/0.65 gt(c, c)
% 0.19/0.65 = { by axiom 3 (succ_pred) R->L }
% 0.19/0.65 gt(succ(pred(c)), c)
% 0.19/0.65 = { by axiom 6 (leq_succ_gt_equiv_1) R->L }
% 0.19/0.65 fresh29(leq(c, pred(c)), true3, c, pred(c))
% 0.19/0.65 = { by axiom 2 (ttrue) R->L }
% 0.19/0.65 fresh29(leq(c, pred(c)), true, c, pred(c))
% 0.19/0.65 = { by axiom 1 (cl5_nebula_norm_0010_1) R->L }
% 0.19/0.65 fresh29(leq(c, pred(pv10)), true, c, pred(c))
% 0.19/0.65 = { by axiom 4 (cl5_nebula_norm_0010_7) }
% 0.19/0.65 fresh29(true3, true, c, pred(c))
% 0.19/0.65 = { by axiom 2 (ttrue) R->L }
% 0.19/0.65 fresh29(true, true, c, pred(c))
% 0.19/0.65 = { by axiom 5 (leq_succ_gt_equiv_1) }
% 0.19/0.65 true3
% 0.19/0.65 = { by axiom 2 (ttrue) R->L }
% 0.19/0.65 true
% 0.19/0.65 = { by axiom 2 (ttrue) }
% 0.19/0.65 true3
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65
% 0.19/0.65 RESULT: Theorem (the conjecture is true).
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