TSTP Solution File: SWV050+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV050+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 : n020.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 23:02:21 EDT 2023
% Result : Theorem 1.27s 0.58s
% Output : Proof 1.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV050+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13 % 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 : n020.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 03:24:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.27/0.58 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 1.27/0.58
% 1.27/0.58 % SZS status Theorem
% 1.27/0.58
% 1.27/0.59 % SZS output start Proof
% 1.27/0.59 Take the following subset of the input axioms:
% 1.27/0.59 fof(cl5_nebula_norm_0022, conjecture, (pv86=sum(n0, minus(n5, n1), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))) & pv88=sum(n0, minus(n5, n1), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89)))))) => (n0=sum(n0, minus(n0, n1), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))) & (pv86=sum(n0, minus(n5, n1), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))) & pv88=sum(n0, minus(n5, n1), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89)))))))).
% 1.27/0.59 fof(pred_minus_1, axiom, ![X]: minus(X, n1)=pred(X)).
% 1.27/0.59 fof(pred_succ, axiom, ![X2]: pred(succ(X2))=X2).
% 1.27/0.59 fof(succ_tptp_minus_1, axiom, succ(tptp_minus_1)=n0).
% 1.27/0.59 fof(sum_plus_base, axiom, ![Body]: sum(n0, tptp_minus_1, Body)=n0).
% 1.27/0.59 fof(sum_plus_base_float, axiom, ![Body2]: tptp_float_0_0=sum(n0, tptp_minus_1, Body2)).
% 1.27/0.59
% 1.27/0.59 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.27/0.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.27/0.59 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.27/0.59 fresh(y, y, x1...xn) = u
% 1.27/0.59 C => fresh(s, t, x1...xn) = v
% 1.27/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 1.27/0.59 variables of u and v.
% 1.27/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.27/0.59 input problem has no model of domain size 1).
% 1.27/0.59
% 1.27/0.59 The encoding turns the above axioms into the following unit equations and goals:
% 1.27/0.59
% 1.27/0.59 Axiom 1 (succ_tptp_minus_1): succ(tptp_minus_1) = n0.
% 1.27/0.59 Axiom 2 (pred_succ): pred(succ(X)) = X.
% 1.27/0.59 Axiom 3 (pred_minus_1): minus(X, n1) = pred(X).
% 1.27/0.59 Axiom 4 (sum_plus_base_float): tptp_float_0_0 = sum(n0, tptp_minus_1, X).
% 1.27/0.59 Axiom 5 (sum_plus_base): sum(n0, tptp_minus_1, X) = n0.
% 1.27/0.59 Axiom 6 (cl5_nebula_norm_0022): pv86 = sum(n0, minus(n5, n1), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))).
% 1.27/0.59 Axiom 7 (cl5_nebula_norm_0022_1): pv88 = sum(n0, minus(n5, n1), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))).
% 1.27/0.59
% 1.27/0.59 Lemma 8: n0 = tptp_float_0_0.
% 1.27/0.59 Proof:
% 1.27/0.59 n0
% 1.27/0.59 = { by axiom 5 (sum_plus_base) R->L }
% 1.27/0.59 sum(n0, tptp_minus_1, X)
% 1.27/0.59 = { by axiom 4 (sum_plus_base_float) R->L }
% 1.27/0.59 tptp_float_0_0
% 1.27/0.59
% 1.27/0.59 Goal 1 (cl5_nebula_norm_0022_2): tuple2(n0, pv86, pv88) = tuple2(sum(n0, minus(n0, n1), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(n0, minus(n5, n1), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(n0, minus(n5, n1), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89)))))).
% 1.27/0.59 Proof:
% 1.27/0.59 tuple2(n0, pv86, pv88)
% 1.27/0.59 = { by lemma 8 }
% 1.27/0.59 tuple2(tptp_float_0_0, pv86, pv88)
% 1.27/0.59 = { by axiom 4 (sum_plus_base_float) }
% 1.27/0.59 tuple2(sum(n0, tptp_minus_1, divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), pv86, pv88)
% 1.27/0.59 = { by lemma 8 }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, tptp_minus_1, divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), pv86, pv88)
% 1.27/0.59 = { by axiom 2 (pred_succ) R->L }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(succ(tptp_minus_1)), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), pv86, pv88)
% 1.27/0.59 = { by axiom 1 (succ_tptp_minus_1) }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(n0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), pv86, pv88)
% 1.27/0.59 = { by lemma 8 }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(tptp_float_0_0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), pv86, pv88)
% 1.27/0.59 = { by axiom 7 (cl5_nebula_norm_0022_1) }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(tptp_float_0_0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), pv86, sum(n0, minus(n5, n1), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by lemma 8 }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(tptp_float_0_0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), pv86, sum(tptp_float_0_0, minus(n5, n1), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by axiom 3 (pred_minus_1) }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(tptp_float_0_0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), pv86, sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by axiom 6 (cl5_nebula_norm_0022) }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(tptp_float_0_0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(n0, minus(n5, n1), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by lemma 8 }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(tptp_float_0_0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(tptp_float_0_0, minus(n5, n1), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by axiom 3 (pred_minus_1) }
% 1.27/0.59 tuple2(sum(tptp_float_0_0, pred(tptp_float_0_0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by lemma 8 R->L }
% 1.27/0.59 tuple2(sum(n0, pred(tptp_float_0_0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by lemma 8 R->L }
% 1.27/0.59 tuple2(sum(n0, pred(n0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by lemma 8 R->L }
% 1.27/0.59 tuple2(sum(n0, pred(n0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(n0, pred(n5), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(tptp_float_0_0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.59 = { by lemma 8 R->L }
% 1.27/0.59 tuple2(sum(n0, pred(n0), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(n0, pred(n5), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(n0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.60 = { by axiom 3 (pred_minus_1) R->L }
% 1.27/0.60 tuple2(sum(n0, minus(n0, n1), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(n0, pred(n5), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(n0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.60 = { by axiom 3 (pred_minus_1) R->L }
% 1.27/0.60 tuple2(sum(n0, minus(n0, n1), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(n0, minus(n5, n1), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(n0, pred(n5), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.60 = { by axiom 3 (pred_minus_1) R->L }
% 1.27/0.60 tuple2(sum(n0, minus(n0, n1), divide(abs(minus(a_select2(sigma, pv91), a_select2(sigmaold, pv91))), plus(abs(a_select2(sigma, pv91)), abs(a_select2(sigmaold, pv91))))), sum(n0, minus(n5, n1), divide(abs(minus(a_select2(mu, pv87), a_select2(muold, pv87))), plus(abs(a_select2(mu, pv87)), abs(a_select2(muold, pv87))))), sum(n0, minus(n5, n1), divide(abs(minus(a_select2(rho, pv89), a_select2(rhoold, pv89))), plus(abs(a_select2(rho, pv89)), abs(a_select2(rhoold, pv89))))))
% 1.27/0.60 % SZS output end Proof
% 1.27/0.60
% 1.27/0.60 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------