TSTP Solution File: SWV074+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV074+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 23:02:27 EDT 2023
% Result : Theorem 0.22s 0.63s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV074+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.08/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 09:02:22 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.63 Command-line arguments: --no-flatten-goal
% 0.22/0.63
% 0.22/0.63 % SZS status Theorem
% 0.22/0.63
% 0.22/0.63 % SZS output start Proof
% 0.22/0.63 Take the following subset of the input axioms:
% 0.22/0.63 fof(cl5_nebula_array_0015, conjecture, (leq(n0, pv31) & (leq(n0, pv36) & (leq(pv31, minus(n5, n1)) & leq(pv36, minus(n135300, n1))))) => (leq(n0, pv31) & (leq(n0, pv36) & (leq(pv31, minus(n5, n1)) & leq(pv36, minus(n135300, n1)))))).
% 0.22/0.63 fof(pred_minus_1, axiom, ![X]: minus(X, n1)=pred(X)).
% 0.22/0.63 fof(ttrue, axiom, true).
% 0.22/0.63
% 0.22/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.63 fresh(y, y, x1...xn) = u
% 0.22/0.63 C => fresh(s, t, x1...xn) = v
% 0.22/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.63 variables of u and v.
% 0.22/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.63 input problem has no model of domain size 1).
% 0.22/0.63
% 0.22/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.63
% 0.22/0.63 Axiom 1 (ttrue): true = true3.
% 0.22/0.63 Axiom 2 (pred_minus_1): minus(X, n1) = pred(X).
% 0.22/0.63 Axiom 3 (cl5_nebula_array_0015): leq(n0, pv31) = true3.
% 0.22/0.63 Axiom 4 (cl5_nebula_array_0015_1): leq(n0, pv36) = true3.
% 0.22/0.63 Axiom 5 (cl5_nebula_array_0015_2): leq(pv31, minus(n5, n1)) = true3.
% 0.22/0.63 Axiom 6 (cl5_nebula_array_0015_3): leq(pv36, minus(n135300, n1)) = true3.
% 0.22/0.63
% 0.22/0.63 Goal 1 (cl5_nebula_array_0015_4): tuple(leq(n0, pv31), leq(n0, pv36), leq(pv31, minus(n5, n1)), leq(pv36, minus(n135300, n1))) = tuple(true3, true3, true3, true3).
% 0.22/0.63 Proof:
% 0.22/0.63 tuple(leq(n0, pv31), leq(n0, pv36), leq(pv31, minus(n5, n1)), leq(pv36, minus(n135300, n1)))
% 0.22/0.63 = { by axiom 2 (pred_minus_1) }
% 0.22/0.63 tuple(leq(n0, pv31), leq(n0, pv36), leq(pv31, pred(n5)), leq(pv36, minus(n135300, n1)))
% 0.22/0.63 = { by axiom 2 (pred_minus_1) }
% 0.22/0.63 tuple(leq(n0, pv31), leq(n0, pv36), leq(pv31, pred(n5)), leq(pv36, pred(n135300)))
% 0.22/0.63 = { by axiom 3 (cl5_nebula_array_0015) }
% 0.22/0.63 tuple(true3, leq(n0, pv36), leq(pv31, pred(n5)), leq(pv36, pred(n135300)))
% 0.22/0.63 = { by axiom 1 (ttrue) R->L }
% 0.22/0.63 tuple(true, leq(n0, pv36), leq(pv31, pred(n5)), leq(pv36, pred(n135300)))
% 0.22/0.63 = { by axiom 4 (cl5_nebula_array_0015_1) }
% 0.22/0.63 tuple(true, true3, leq(pv31, pred(n5)), leq(pv36, pred(n135300)))
% 0.22/0.63 = { by axiom 1 (ttrue) R->L }
% 0.22/0.63 tuple(true, true, leq(pv31, pred(n5)), leq(pv36, pred(n135300)))
% 0.22/0.63 = { by axiom 2 (pred_minus_1) R->L }
% 0.22/0.63 tuple(true, true, leq(pv31, minus(n5, n1)), leq(pv36, pred(n135300)))
% 0.22/0.63 = { by axiom 5 (cl5_nebula_array_0015_2) }
% 0.22/0.63 tuple(true, true, true3, leq(pv36, pred(n135300)))
% 0.22/0.63 = { by axiom 1 (ttrue) R->L }
% 0.22/0.63 tuple(true, true, true, leq(pv36, pred(n135300)))
% 0.22/0.63 = { by axiom 2 (pred_minus_1) R->L }
% 0.22/0.63 tuple(true, true, true, leq(pv36, minus(n135300, n1)))
% 0.22/0.63 = { by axiom 6 (cl5_nebula_array_0015_3) }
% 0.22/0.63 tuple(true, true, true, true3)
% 0.22/0.63 = { by axiom 1 (ttrue) R->L }
% 0.22/0.63 tuple(true, true, true, true)
% 0.22/0.63 = { by axiom 1 (ttrue) }
% 0.22/0.63 tuple(true3, true, true, true)
% 0.22/0.63 = { by axiom 1 (ttrue) }
% 0.22/0.63 tuple(true3, true3, true, true)
% 0.22/0.63 = { by axiom 1 (ttrue) }
% 0.22/0.63 tuple(true3, true3, true3, true)
% 0.22/0.63 = { by axiom 1 (ttrue) }
% 0.22/0.63 tuple(true3, true3, true3, true3)
% 0.22/0.63 % SZS output end Proof
% 0.22/0.63
% 0.22/0.63 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------